From 052c5b9e6a8af929c0d270f401e305e6a56cb363 Mon Sep 17 00:00:00 2001 From: = Date: Thu, 11 Apr 2024 11:08:02 -0400 Subject: [PATCH 1/4] fix typo --- examples/Ising.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/Ising.ipynb b/examples/Ising.ipynb index 79052b7..093c0a5 100644 --- a/examples/Ising.ipynb +++ b/examples/Ising.ipynb @@ -10,7 +10,7 @@ "The Model Hamiltonian Package is a software tool designed to generate 0, 1, and 2 electron integrals for various quantum models. In this tutorial, we'll focus on generating integrals for the Heisenberg model, specifically the XXZ Heisenberg model.\n", "\n", "## XXZ Heisenberg Model\n", - "The XXZ Heisenberg model is a one-dimensional quantum model that describes the interaction between spins on a lattice. The Hamiltonian for the XXZ Heisenberg model is given by:\n", + "The XXZ Heisenberg model is a quantum model that describes the interaction between spins on a lattice. The Hamiltonian for the XXZ Heisenberg model is given by:\n", "$$\n", "\\hat{H}_{X X Z}=\\sum_p\\left(\\mu_p^Z-J_{p p}^{\\mathrm{eq}}\\right) S_p^Z+\\sum_{p \\neq q} J_{p q}^{\\mathrm{ax}} S_p^Z S_q^Z+\\sum_{p \\neq q} J_{p q}^{\\mathrm{eq}} S_p^{+} S_q^{-}\n", "$$\n", From 7fc239a055a7727efd68e6cf4ac18830caa2d646 Mon Sep 17 00:00:00 2001 From: = Date: Thu, 11 Apr 2024 16:07:34 -0400 Subject: [PATCH 2/4] add savez method --- moha/api.py | 32 +++++++++++++++++++++++++++++--- moha/hamiltonians.py | 3 +++ 2 files changed, 32 insertions(+), 3 deletions(-) diff --git a/moha/api.py b/moha/api.py index 2770193..5abc6d0 100644 --- a/moha/api.py +++ b/moha/api.py @@ -367,9 +367,35 @@ def save_triqs(self, fname: str, integral): """ pass - def save(self, fname: str, integral, basis): - r"""Save file as regular numpy array.""" - pass + def savez(self, fname: str): + r"""Save file as regular npz file. + + Parameters + ---------- + fname: str + name of the file + + Returns + ------- + None + """ + if self.zero_energy is not None: + e0 = self.zero_energy + else: + raise ValueError("Zero energy was not calculated.") + + if self.one_body is not None: + h = self.to_dense(self.one_body, dim=2) + else: + raise ValueError("One body integrals were not calculated.") + + if self.two_body is not None: + v = self.to_dense(self.two_body, dim=4) + else: + raise ValueError("Two body integrals were not calculated.") + + np.savez(fname, e0=e0, h1=h, h2=v) + def expand_sym(sym, integral, nbody): diff --git a/moha/hamiltonians.py b/moha/hamiltonians.py index e9daf61..a152150 100644 --- a/moha/hamiltonians.py +++ b/moha/hamiltonians.py @@ -105,6 +105,7 @@ def generate_zero_body_integral(self): float """ if self.charges is None or self.gamma is None: + self.zero_energy = 0 return 0 else: self.zero_energy = 0.5 * self.charges @ self.gamma @ self.charges @@ -410,6 +411,7 @@ def __init__(self, self.zero_energy = None self.one_body = None self.two_body = None + self._sym = 1 def generate_zero_body_integral(self): """ @@ -421,6 +423,7 @@ def generate_zero_body_integral(self): """ zero_energy = -0.5 * np.sum(self.mu - np.diag(self.J_eq)) \ + 0.25 * np.sum(self.J_ax)/2 # divide by 2 to avoid double counting # noqa: E501 + self.zero_energy = zero_energy return zero_energy def generate_one_body_integral(self, From d96c5498ecf22db73fc818c21949c4cc9da9a411 Mon Sep 17 00:00:00 2001 From: = Date: Thu, 11 Apr 2024 16:08:28 -0400 Subject: [PATCH 3/4] add Tutorials --- examples/Demonstration.ipynb | 644 ++++++++++++----------------------- examples/Ising.ipynb | 48 ++- 2 files changed, 267 insertions(+), 425 deletions(-) diff --git a/examples/Demonstration.ipynb b/examples/Demonstration.ipynb index b8f3fc9..bbb6362 100644 --- a/examples/Demonstration.ipynb +++ b/examples/Demonstration.ipynb @@ -7,499 +7,251 @@ "id": "875c2738" }, "source": [ - "# Demonstration of the Model Hamiltonian" - ] - }, - { - "cell_type": "markdown", - "id": "2e94e90d", - "metadata": { - "id": "2e94e90d" - }, - "source": [ - "## Theoretical intro" + "# Tutorial: Occupation-based Hamiltionians\n", + "\n", + "## Introduction\n", + "The Model Hamiltonian Package is a software tool designed to generate 0, 1, and 2 electron integrals for various quantum models. In this tutorial, we'll focus on generating integrals for the occupation-based hamiltonians, specifically on Hubbard hamiltonian." ] }, { "cell_type": "markdown", - "id": "6c918307", - "metadata": { - "id": "6c918307" - }, + "id": "2f54d140", + "metadata": {}, "source": [ - "The basic purpose of Model Hamiltonians is that in many cases, the low-energy spectrum and qualitative features of a complicated many-body system can be approximated by a simplified model Hamiltonian. This most frequently occurs when the state of every atom/site/group/moiety in a molecule/crystal can be well described by its occupation and/or spin. \n", - "> An excellent introduction to this strategy can be found in [B. J. Powell, \"An introduction to effective low-energy hamiltonians in condensed matter physics and chemistry.\" In: *Computational methods for large systems: electronic structure approaches for biotechnology and nanotechnology*, J. R. Reimers, editor; (Hoboken, Wiley, 2011). Chapter 1, 309–366.](https://arxiv.org/pdf/0906.1640.pdf)\n", - "\n", - "## Objectives\n", - "Many model Hamiltonians can be cast into a form that is conveniently solved by standard quantum-chemistry packages. The goal of this package is to automate this transformation. The objectives are to:\n", - "- Make it simple for users to specify model Hamiltonians. \n", - "- Provide support for `FCIDump` files through the link between `gbasis` and [`IOData`](iodata.qcdevs.org). \n", - "- (Longer term) Provide benchmark data for certain model Hamiltonians, which can be used for assessing approximate methods for solving the corresponding Schrödinger equations.\n", - " \n", - "## Quantum Chemistry Hamiltonian (Gaby)\n", - "The quantum chemistry Hamiltonian consists of 1- and 2-electron integrals. The normal form, in second quantization, is \n", - "$$\n", - "\\hat{H} = \\sum_{pq} h_{pq} a_p^{\\dagger} a_q + \\tfrac{1}{2} \\sum_{pqrs} g_{pqrs} a_p^{\\dagger} a_q^{\\dagger} a_s a_r\n", - "$$\n", - "This equation chooses the orbital-indexing convention from [Molecular Electronic Structure Theory (Helgaker, Jorgensen, Olsen)](https://onlinelibrary.wiley.com/doi/book/10.1002/9781119019572). The sums are over spin-orbitals,\n", - "$$\n", - "\\phi_p(\\mathbf{r})|\\sigma_p \\rangle = a_p^{\\dagger} |\\text{vacuum}\\rangle\n", - "$$\n", - "in some cases it is important to explicitly denote spin. Even though it makes our notation a little clunky, in these cases we choose to explicitly declare the spin. E.g. we'll write $a_{p\\alpha}^{\\dagger}$ or $a_{q\\beta}$. When spin is not specified, the default is to assume that all spin-orbital interactions are the same except for where they must vanish by symmetry. I.e.,\n", - "$$\n", - "h_{p\\alpha, q\\alpha} = h_{p\\beta, q\\beta} = h_{pq} \\\\ \n", - "h_{p\\alpha, q\\beta} = h_{p\\beta, q\\alpha} = 0 \n", - "$$\n", - "$$\n", - "g_{p\\alpha, q\\alpha, r \\alpha, s\\alpha} = g_{p\\beta, q\\beta, r \\beta, s\\beta} = g_{p\\alpha, q\\alpha, r \\beta, s\\beta} = g_{p\\beta, q\\beta, r \\alpha, s\\alpha} = g_{pqrs}\\\\ \n", - "$$\n", - "In addition, one has that:\n", - "$$\n", - "g_{p \\sigma_p, q \\sigma_q, r \\sigma_r, s \\sigma_s,} = 0 \\qquad \\text{ if } \\sigma_p \\ne \\sigma_q \\text{ and/or } \\sigma_r \\ne \\sigma_s \n", - "$$\n", - "There are also matrix elements that must be identical by symmetry because we assume that orbitals are real-valued:\n", - "$$\n", - "h_{pq} = h_{qp} \\\\\n", - "g_{pqrs} = g_{rspq} = g_{qprs} = g_{rsqp} = g_{pqsr} = g_{srpq} = g_{qpsr} = g_{srqp}\n", - "$$\n", - "\n", - "## Model Hamiltonians Based on Occupation Numbers\n", - "In many cases, this form is rather impractical. For example, there may be only a few \"key\" electrons, and the remaining electrons could then be treated with an effective Hamiltonian (on top of a \"frozen core\") of other orbitals. For example, in some cases, it is more convenient to think only about the occupation number of a atomic (or functional moiety) site in a molecule in a crystal, or only the spin of the site. Occupation numbers are easily written in terms of the second-quantized operators,\n", - "$$\n", - "\\hat{n}_p = a_p^\\dagger a_p\n", + "The most general occupation-number Hamiltonian we consider is the generalized Pariser-Parr-Pople (PPP) Hamiltonian, \n", "$$\n", - "The most general occupation-number-ish Hamiltonian we consider is the generalized Pariser-Parr-Pople + pairing (PPP+P) Hamiltonian, \n", + "\\hat{H}_{\\text{PPP}} = \\sum_{pq} h_{pq} a_p^\\dagger a_q + \\sum_p U_p \\hat{n}_{p\\alpha}\\hat{n}_{p\\beta} + \\frac{1}{2}\\sum_{p\\ne q} \\gamma_{pq} (\\hat{n}_{p \\alpha} + \\hat{n}_{p \\beta} - Q_p)(\\hat{n}_{q \\alpha} + \\hat{n}_{q \\beta} - Q_q) \n", "$$\n", - "\\hat{H}_{\\text{PPP+P}} = \\sum_{pq} h_{pq} a_p^\\dagger a_q + \\sum_p U_p \\hat{n}_{p\\alpha}\\hat{n}_{p\\beta} + \\frac{1}{2}\\sum_{p\\ne q} \\gamma_{pq} (\\hat{n}_{p \\alpha} + \\hat{n}_{p \\beta} - Q_p)(\\hat{n}_{q \\alpha} + \\hat{n}_{q \\beta} - Q_q) + \\sum_{p \\ne q} g_{pq} a_{p \\alpha}^\\dagger a_{p \\beta}^\\dagger a_{q \\beta} a_{q \\alpha}\n", - "$$\n", - "This Hamiltonian has seniority zero if $h_{p \\ne q} = 0$. It includes all possible seniority-zero Hamiltonians. \n", - "\n", "The first terms, $h_{pq}$, could be anything, but are usually approximated at the level of [Hückel theory](notes/huckel-model-hamiltonian.md). (In the solid-state literature, these are usually denoted $h_{pq} = t_{pq}$.) The $U_p$ term denotes the repulsion of electrons on the same atom/group site, whilst the $\\gamma_{pq}$ term denotes the interaction between electrons and (possibly charged; usually $Q_p = 1$ so that the net charge of a system with one electron per site is zero) and other sites (including electrons on those sites). The $g_{pq}$ term captures interactions between electron pairs; the $g_{pq}$ term is redundant with the on-site repulsion, $g_{pp} = U_p$. \n", "\n", - "Special cases of this Hamiltonian include:\n", - "- **Pariser-Parr-Pople (PPP).** The PPP model is obtained when one chooses $g_{pq} = 0$. It can be invoked by choosing `g_pair = 0`.\n", - "- **extended Hubbard.** The extended Hubbard model corresponds to choosing $Q_p = 0$. It can be invoked by choosing `charges = 0` and `g_pair = 0`. \n", + "In ModelHamiltonian package we support some special cases of this Hamiltonian:\n", "- **Hubbard.** The Hubbard model corresponds to choosing $\\gamma_{pq} = 0$. It can be invoked by choosing `gamma = 0`. \n", - "- **Hückle.** [The Hückle model](notes/huckel-model-hamiltonian.md) corresponds to choosing $U_p = \\gamma_{pq} = 0$. It can be invoked by choosing `U_onsite = 0` and `gamma = 0`. \n", - "- **electronegativity equalization.** The electronegativity equalization model has a specific form, which can be cast in this form when $g_{pq} = h_{p \\ne q} = 0$. \n", - "- **addition of a magnetic field (isn't supported yet).** A uniform magnetic field oriented in the $z$ direction, $B_z$, splits the one-electron energy levels by:\n", - "$$\n", - "h_{p \\alpha, p \\alpha} \\rightarrow h_{p \\alpha, p \\alpha} + \\tfrac{g_e}{2} B_z \\\\\n", - "h_{p \\beta, p \\beta} \\rightarrow h_{p \\beta, p \\beta} - \\tfrac{g_e}{2}B_z\n", - "$$\n", - "Here $g_e = 2.00231$ is the g-factor for the electron (`scipy.constants.value(\"electron g factor\")`)." + "- **Hückle.** [The Hückle model](notes/huckel-model-hamiltonian.md) corresponds to choosing $U_p = \\gamma_{pq} = 0$. It can be invoked by choosing `U_onsite = 0` and `gamma = 0`. " ] }, { - "attachments": {}, "cell_type": "markdown", - "id": "3666027d", - "metadata": { - "id": "3666027d" - }, + "id": "cb00b545", + "metadata": {}, "source": [ + "## Example: Defining Hubbard Hamiltonian\n", + "There are two ways to define any occupation-based hamiltonian using the Model Hamiltonian Package:\n", + "1. Using the connectivity matrix of the lattice\n", + "2. Prividing connectivity as a list of tuples, in which atoms are specified along with connectivity type\n", "\n", - "## Example: Polyene Molecule\n", - "\n", - "\n", - "One of the simplest polyene molecules which we can use to test our model hamiltonian construction is benzene, of which the π-electrons each have significant coupling as denoted in the picture below.\n", - "\n", - "\n", - "\n", - "Following e.g. [J. Chem. Phys. 108, 9246 (1998)](https://doi.org/10.1063/1.476379) and [J. Quantum Chem. 51, 13-25 (1994)](https://doi.org/10.1002/qua.560510104), the hamiltonian for a polyene molecule can be written as\n", - "\n", - "$$\n", - "H = \\beta \\sum_{\\langle pq \\rangle} a^{\\dagger}_p a_q + \\frac{1}{2} \\sum_{pq} \\gamma_{pq}(n_p - 1)(n_q - 1)\n", - "$$\n", - "\n", - "which is a special case of the PPP+P hamiltonian. For benzene, $\\beta = -2.5$ eV and $\\gamma_{pq}$ is given by\n", - "\n", - "$$\n", - "\\gamma_{pq} = \\frac{1}{\\gamma_0^{-1} - d_{pq}}\n", - "$$\n", - "\n", - "where $\\gamma_0 = 10.84$ eV and $d_{pq}$ is the C-C separation distance, which for cyclic polyenes is given by\n", - "\n", - "$$\n", - "d_{pq} = b\\frac{\\sin(|p-q|\\pi/N)}{\\sin(\\pi/N)}\n", - "$$\n", - "\n", - "with $b=1.4$ Å for benzene in particular.\n", - "\n", - "We need to identify the zero-body, one-body, and two-body hamiltonian matrix elements to use as input for quantum chemistry software - this process is automated for us in moha. The hamiltonian for polyene can, of course, be written in the general quantum chemistry form\n", - "\n", - "$$\n", - "H = h^{(0)} + \\sum_{pq} h^{(1)}_{pq} a_p^{\\dagger} a_q + \\sum_{pqrs} h^{(2)}_{pqrs} a_p^{\\dagger} a_q a_s^{\\dagger} a_r\n", - "$$\n", - "\n", - "where\n", - "\n", - "\\begin{align}\n", - "h^{(0)} &= \\frac{1}{2}\\sum_{pq} \\gamma_{pq}, \\quad \n", - "h^{(1)}_{pq} = (\\delta_{pq+ 1}+\\delta_{pq-1})\\beta - \\delta_{pq}\\sum_{p}\\gamma_{pq}, \\ \\ \\text{and} \\quad\n", - "h^{(2)}_{pqrs} = \\frac{1}{2}\\gamma_{pr}\\delta_{pq}\\delta_{rs}\n", - "\\end{align}\n", - "\n", - "We demonstrate below how the hamiltonian terms can be calculated by hand and compare with how they may be generated using the moha library." + "Any occupation-base model requires energy of the orbital, $\\alpha$, and interaction energy between nearest orbitals, $\\beta$. By default, the energy of the orbital is set to -0.414 eV that corresponds to the energy of electron in a 2p orbital, and the interaction energy is set to -0.0533 eV that corresponds to the interaction energy between nearest 2p orbitals." ] }, { "cell_type": "code", - "execution_count": 5, - "id": "9e9d37ef", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "9e9d37ef", - "outputId": "0c506bb1-6bca-44cd-afef-ff56ac5f0da7", - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "h0=\n", - " 39.962 \n", - "\n", - "h1=\n", - " [[-13.321 -2.5 0. 0. 0. -2.5 ]\n", - " [ -2.5 -13.321 -2.5 0. 0. 0. ]\n", - " [ 0. -2.5 -13.321 -2.5 0. 0. ]\n", - " [ 0. 0. -2.5 -13.321 -2.5 0. ]\n", - " [ 0. 0. 0. -2.5 -13.321 -2.5 ]\n", - " [ -2.5 0. 0. 0. -2.5 -13.321]] \n", - "\n", - "h2=\n", - " [[5.42 0.335 0.199 0.173 0.199 0.335]\n", - " [0.335 5.42 0.335 0.199 0.173 0.199]\n", - " [0.199 0.335 5.42 0.335 0.199 0.173]\n", - " [0.173 0.199 0.335 5.42 0.335 0.199]\n", - " [0.199 0.173 0.199 0.335 5.42 0.335]\n", - " [0.335 0.199 0.173 0.199 0.335 5.42 ]] \n", - "\n" - ] - } - ], + "execution_count": 1, + "id": "36ebc326", + "metadata": {}, + "outputs": [], "source": [ + "# import libraries\n", + "from moha import HamHub\n", "import numpy as np\n", "\n", - "### Function for printing the hamiltonian\n", - "def print_hamiltonian(h0, h1, h2):\n", - " np.set_printoptions(precision=3)\n", - " print('h0=\\n',\"%0.3f\" % h0,'\\n') \n", - " print('h1=\\n',h1,'\\n')\n", - " print('h2=\\n',h2,'\\n')\n", - "\n", - "### Gamma value generator for polyene\n", - "def generate_gamma(norb, b, gamma0): \n", - " ang_to_bohr = 1.889726\n", - " har_to_ev = 27.211396\n", - " b_ieV = b*ang_to_bohr/har_to_ev\n", - "\n", - " gamma = np.zeros((norb,norb))\n", - " for u in range(norb):\n", - " for v in range(norb):\n", - " duv = b*(np.sin(abs(u-v)*np.pi/norb)/np.sin(np.pi/norb))\n", - " gamma[(u,v)] = 1/(1/gamma0 + duv)\n", - "\n", - " return gamma \n", - " \n", - "### Building integral arrays for benzene\n", - "norb = 6\n", - "b = 1.4\n", - "gamma0 = 10.84\n", - "beta = -2.5\n", - "\n", - "gamma = generate_gamma(norb, b, gamma0)\n", - "gamma0 = gamma[0,0]\n", - "\n", - "h1 = np.zeros([norb,norb])\n", - "for n in range(norb):\n", - " h1[(n,(n+1)%norb)] = beta\n", - "h1 += h1.T\n", - "\n", - "h0 = 0\n", - "h2 = np.zeros((norb,norb,norb,norb))\n", - "H2 = np.zeros([norb,norb])\n", - "for n in range(norb):\n", - " h1[(n,n)] -= np.sum(gamma[n,:])\n", - " for m in range(norb):\n", - " h2[(n,n,m,m)] = 0.5*gamma[(n,m)]\n", - " H2[n,m] = h2[(n,n,m,m)]\n", - " h0 += 0.5*gamma[(n,m)]\n", - "\n", - "print_hamiltonian(h0, h1, H2)" + "# First way to define the Hamiltonian\n", + "# two site Hubbard model\n", + "\n", + "# system = [('C1', 'C2', 1)] is a list of tuples, where each tuple represents a bond\n", + "# between two atoms and the third element is the type of bond (singe or double).\n", + "# For now, we only support single bonds between carbon atoms. \n", + "# For this type of bonds the default values of alpha and beta are -0.414 and -0.0533, respectively.\n", + "# In the future we are planning to support different types of bonds for different atoms.\n", + "system = [('C1', 'C2', 1)]\n", + "hubbard = HamHub(system,\n", + " alpha=-0.414, beta=-0.0533, u_onsite=np.array([1, 1]))\n", + "\n", + "# Second way to define the Hamiltonian\n", + "# two site Hubbard model\n", + "connectivity = np.array([[0, 1],\n", + " [1, 0]])\n", + "hubbard = HamHub(connectivity,\n", + " alpha=-0.414, beta=-0.0533, u_onsite=np.array([1, 1]))" ] }, { "cell_type": "markdown", - "id": "b6b37731", - "metadata": { - "id": "b6b37731" - }, + "id": "58ca55f1", + "metadata": {}, "source": [ - "### Using MoHa" + "## Generating Integrals\n", + "The Model Hamiltonian Package can generate 0, 1, and 2 electron integrals for the PPP model Hamiltonian. The integrals are stored in a sparse matrix format, and can be used to solve the Schrödinger equation for the model.\n", + "Specifically, the integrals support the following operations:\n", + "1. Get the 0, 1, and 2 electron integrals for the PPP model;\n", + "2. Return intergrals in the form of a sparse or dense matrix;\n", + "3. Return integrals in a spin orbital or spatial basis; \n", + "\n", + " __Note__ : Assumption is alpha and beta spinorbitals are the same;\n", + "4. Support 1-, 2-, 4- , and 8-fold symmetry such as:\n", + "\n", + " a. 1-fold symmetry: no symmetry;\n", + " \n", + " b. 2-fold symmetry: $$g_{ij,kl} = g_{kl,ij}$$\n", + " c. 4-fold symmetry: $$g_{ij,kl} = g_{kl,ij} = g_{ji,lk} = g_{lk,ji} $$\n", + " d. 8-fold symmetry: $$g_{ij,kl} = g_{kl,ij} = g_{ji,lk} = g_{lk,ji} = g_{ji,kl} = g_{kl,ji} = g_{ij,lk} = g_{lk,ij} $$" ] }, { "cell_type": "code", - "execution_count": 6, - "id": "1eeff845", - "metadata": { - "id": "1eeff845", - "outputId": "8fee4217-734e-4870-e56f-9392fdb5317e" - }, + "execution_count": 2, + "id": "21b6dc5e", + "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "h0=\n", - " 39.962 \n", - "\n", - "h1=\n", - " [[-13.321 -2.5 0. 0. 0. -2.5 ]\n", - " [ -2.5 -13.321 -2.5 0. 0. 0. ]\n", - " [ 0. -2.5 -13.321 -2.5 0. 0. ]\n", - " [ 0. 0. -2.5 -13.321 -2.5 0. ]\n", - " [ 0. 0. 0. -2.5 -13.321 -2.5 ]\n", - " [ -2.5 0. 0. 0. -2.5 -13.321]] \n", - "\n", - "h2=\n", - " (0, 0)\t5.42\n", - " (1, 1)\t0.3350642927794263\n", - " (2, 2)\t0.1986395532084328\n", - " (3, 3)\t0.1728757336055116\n", - " (4, 4)\t0.1986395532084328\n", - " (5, 5)\t0.3350642927794263\n", - " (7, 7)\t5.42\n", - " (8, 8)\t0.3350642927794263\n", - " (9, 9)\t0.1986395532084328\n", - " (10, 10)\t0.1728757336055116\n", - " (11, 11)\t0.1986395532084328\n", - " (14, 14)\t5.42\n", - " (15, 15)\t0.3350642927794263\n", - " (16, 16)\t0.1986395532084328\n", - " (17, 17)\t0.1728757336055116\n", - " (21, 21)\t5.42\n", - " (22, 22)\t0.3350642927794263\n", - " (23, 23)\t0.1986395532084328\n", - " (28, 28)\t5.42\n", - " (29, 29)\t0.3350642927794263\n", - " (35, 35)\t5.42 \n", - "\n" + "Zero energy: 0\n", + "One body integrals in spatial basis: \n", + " [[ 0. -1. 0. 0. 0. -1.]\n", + " [-1. 0. -1. 0. 0. 0.]\n", + " [ 0. -1. 0. -1. 0. 0.]\n", + " [ 0. 0. -1. 0. -1. 0.]\n", + " [ 0. 0. 0. -1. 0. -1.]\n", + " [-1. 0. 0. 0. -1. 0.]]\n", + "Shape of two body integral in spatial basis: (6, 6, 6, 6)\n", + "------------------------------------------------------------\n", + "One body integrals in spin basis: \n", + " [[ 0. -1. 0. 0. 0. -1. 0. 0. 0. 0. 0. 0.]\n", + " [-1. 0. -1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [ 0. -1. 0. -1. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [ 0. 0. -1. 0. -1. 0. 0. 0. 0. 0. 0. 0.]\n", + " [ 0. 0. 0. -1. 0. -1. 0. 0. 0. 0. 0. 0.]\n", + " [-1. 0. 0. 0. -1. 0. 0. 0. 0. 0. 0. 0.]\n", + " [ 0. 0. 0. 0. 0. 0. 0. -1. 0. 0. 0. -1.]\n", + " [ 0. 0. 0. 0. 0. 0. -1. 0. -1. 0. 0. 0.]\n", + " [ 0. 0. 0. 0. 0. 0. 0. -1. 0. -1. 0. 0.]\n", + " [ 0. 0. 0. 0. 0. 0. 0. 0. -1. 0. -1. 0.]\n", + " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. -1. 0. -1.]\n", + " [ 0. 0. 0. 0. 0. 0. -1. 0. 0. 0. -1. 0.]]\n", + "Shape of two body integral in spinorbital basis: (12, 12, 12, 12)\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/anaconda3/lib/python3.9/site-packages/scipy/sparse/_index.py:100: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n", + " self._set_intXint(row, col, x.flat[0])\n" ] } ], "source": [ - "import sys \n", - "sys.path.insert(0, '../')\n", - "\n", - "from moha import HamPPP\n", - "\n", - "polyene = HamPPP([(f\"C{i}\", f\"C{i + 1}\", 1) for i in range(1, norb)] + [(f\"C{norb}\", f\"C{1}\", 1)],\n", - " alpha=0, beta=beta, gamma=gamma, charges=np.ones(6),\n", - " u_onsite=np.array([0.5*gamma0 for i in range(norb + 1)]))\n", - "\n", - "h0 = polyene.generate_zero_body_integral()\n", - "h1 = polyene.generate_one_body_integral(dense=True, basis='spatial basis')\n", - "h2 = polyene.generate_two_body_integral(dense=False, basis='spatial basis')\n", - "\n", - "print_hamiltonian(h0, h1, h2)" + "# Example: generating 6 site Hubbard model \n", + "# Returning electron integrals in a spatial orbital basis\n", + "# Assuming 8-fold symmetry\n", + "# Returning output as dense matrix\n", + "\n", + "connectivity = np.array([[0, 1, 0, 0, 0, 1],\n", + " [1, 0, 1, 0, 0, 0],\n", + " [0, 1, 0, 1, 0, 0],\n", + " [0, 0, 1, 0, 1, 0],\n", + " [0, 0, 0, 1, 0, 1],\n", + " [1, 0, 0, 0, 1, 0]])\n", + "hubbard = HamHub(connectivity,\n", + " alpha=0, \n", + " beta=-1, \n", + " u_onsite=np.array([1, 1, 1, 1, 1, 1]))\n", + "\n", + "e0 = hubbard.generate_zero_body_integral()\n", + "h1 = hubbard.generate_one_body_integral(dense=True, basis='spatial basis') \n", + "h2 = hubbard.generate_two_body_integral(dense=True, basis='spatial basis', sym=8)\n", + "\n", + "print(\"Zero energy: \", e0)\n", + "print(\"One body integrals in spatial basis: \\n\", h1)\n", + "print(\"Shape of two body integral in spatial basis: \", h2.shape)\n", + "print(\"-\"*60)\n", + "\n", + "# Example: generating Hubbard model in spin orbital basis\n", + "# Assuming 8-fold symmetry\n", + "# Returning output as dense matrix\n", + "\n", + "h1 = hubbard.generate_one_body_integral(dense=True, basis='spinorbital basis')\n", + "h2 = hubbard.generate_two_body_integral(dense=True, basis='spinorbital basis', sym=4)\n", + "\n", + "print(\"One body integrals in spin basis: \\n\", h1)\n", + "print(\"Shape of two body integral in spinorbital basis: \", h2.shape)" ] }, { "cell_type": "markdown", - "id": "43ae7996", + "id": "55b7e2b9", "metadata": {}, "source": [ - "The result can then be saved to FCIDUMP format and used in quantum chemistry software by using, for example,\n", - "\n", - " filename = \"polyene.dat\"\n", - " fout = open(filename, \"w\")\n", - " polyene.save_fcidump(f=fout, nelec=norb)" - ] - }, - { - "cell_type": "markdown", - "id": "cd75406a", - "metadata": { - "id": "cd75406a" - }, - "source": [ - "## Define the system:\n", - "\n", - "1. Connectivity of the system is defined as list of tuples of atoms that are connected. For example, two carbon atoms are connected by single bond can be defined as\n", - "```\n", - "[('C1', 'C2')]\n", - "```\n", - "3 carbon atoms that creates triangle can be defined as \n", - "```\n", - "[('C1', 'C2'), ('C2', 'C3'), ('C3', 'C2')]\n", - "```\n", - "\n", - "2. Additional parameters could be specified using the following arguments:\n", - " 1. alpha, beta - correspondent parameters from [Hückel method](https://en.wikipedia.org/wiki/Hückel_method)\n", - " 2. u_onsite - potential on each site of the system \n", - " 3. gamma - parameter that denotes interaction within electrons\n", - " 4. charges - charge on the site\n", + "# Testing the Hubbard model\n", "\n", + "To test the ouput of the ModelHamiltoian package, we can solve the Schrödinger equation using Full CI algorithm fron the `pyscf` package.\n", "\n", - "## Get zero-, one-, two- body term:\n", - "\n", - "Ones hamiltonian is built, getting one and two body term of hamiltonian and energy of the system is breeze! All nessesary methods are:\n", - "```\n", - "hamiltonian.generate_one_body_integral(*parameters)\n", - "hamiltonian.generate_two_body_integral(*parameters)\n", - "hamiltonian.generate_zero_body_integral(*parameters)\n", - "```\n", - "\n", - "### Parameters for specifying output hamiltonian:\n", - "1. basis: `'spatial basis'` or `'spinorbital basis'`\n", - "2. dense: `True` or `False` format of the output matrix. If True returns np.ndarray otherwise - scipy.sparce.csr matrix\n", + "[It can be shown](https://arxiv.org/pdf/cond-mat/0207529.pdf) that ground state energy in the half-filled one dimensional Hubbard model in the thermodynamic limit is given by Lieb-Wu formula:\n", "\n", + "$$\n", + "E_0=-4 N \\int_0^{\\infty} \\frac{J_0(\\omega) J_1(\\omega)}{\\omega\\left(1+e^{\\omega U / 2}\\right)} d \\omega\n", + "$$\n", "\n", - "## Saving output\n", + "where $N$ is the number of electrons in the chain, $J_0$ and $J_1$ are Bessel functions of the first kind, and $U$ is the on-site repulsion.\n", "\n", - "It's possible to save a Hamiltonian as FCIDUMP file using `hamiltonian.save_fcidump(*parameters)`\n", - "### Parameters for saving the hamiltonian:\n", - "1. TextIO format; highly reccomended to use `open(filename, 'w')`\n", - "2. Number of electrons in the sustem; integer" + "In this section, we will test the convergence of the ground state energy of the Hubbard model with the number of sites in the chain. We will compute the ground state energy obtained from the Model Hamiltonian Package with Full CI algorithm in the `pyscf` package with." ] }, { "cell_type": "code", - "execution_count": 4, - "id": "aeb354f5", - "metadata": { - "id": "aeb354f5", - "outputId": "a07b7db0-e3a4-40bf-90c6-3b17c0d78c8f" - }, + "execution_count": 3, + "id": "b29c77cf", + "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "one body term in spinorbital basis is \n", - " [[ 0. -1. 0. 0.]\n", - " [-1. 0. 0. 0.]\n", - " [ 0. 0. 0. -1.]\n", - " [ 0. 0. -1. 0.]]\n", - "one body term in spinorbital basis is \n", - " (0, 1)\t-1.0\n", - " (1, 0)\t-1.0\n", - "two body term in spinorbital basis is \n", - " [[[[1. 0.]\n", - " [0. 0.]]\n", - "\n", - " [[0. 0.]\n", - " [0. 0.]]]\n", - "\n", - "\n", - " [[[0. 0.]\n", - " [0. 0.]]\n", - "\n", - " [[0. 0.]\n", - " [0. 1.]]]]\n" + "Energy given by Lieb-Wu formula: -1.040368653394435\n", + "Error of integration: 8.675915091601108e-11\n" ] } ], "source": [ - "### two site Hubbard model\n", - "system = [('C1', 'C2', 1)]\n", - "hubbard = HamHub(system,\n", - " alpha=0, beta=-1, u_onsite=np.array([1, 1]))\n", - "\n", - "### generating one body term in spinorbital basis\n", - "h_spin = hubbard.generate_one_body_integral(dense=True, basis='spinorbital basis')\n", - "print('one body term in spinorbital basis is \\n', h_spin)\n", - "\n", - "### generating one body term in spatial basis sparse output\n", - "h_sparse = hubbard.generate_one_body_integral(dense=False, basis='spatial basis')\n", - "print('one body term in spinorbital basis is \\n', h_sparse)\n", - "\n", + "# Computing the energy using the Lieb-Wu formula\n", + "from scipy.integrate import quad\n", + "from scipy.special import *\n", "\n", + "U = []\n", + "E_LW = []\n", "\n", - "### generating two body term in spatial basis\n", - "v_spatial = hubbard.generate_two_body_integral(dense=True, basis='spatial basis')\n", - "print('two body term in spinorbital basis is \\n', v_spatial)\n", + "for Ui in np.linspace(1,10,6):\n", + " Ei, err = quad(lambda x: j0(x) * j1(x) / (x * (1 + np.exp(Ui * x / 2))),0, 100)\n", + " U.append(Ui)\n", + " E_LW.append(-4*Ei)\n", "\n", - "## Saving system\n", - "hubbard.save_fcidump(open('hubbard_2_site.fcidump', 'w'), nelec=1)" + "print(\"Energy given by Lieb-Wu formula: \", E_LW[0])\n", + "print(\"Error of integration: \", err)" ] }, { "cell_type": "markdown", - "id": "708240dc", - "metadata": { - "id": "708240dc" - }, - "source": [ - "## Testing on chain hubbard model with periodic boundary condition" - ] - }, - { - "cell_type": "markdown", - "id": "42345223", - "metadata": { - "id": "42345223" - }, + "id": "4459394a", + "metadata": {}, "source": [ - "This model is described by Lieb Wu formula for an infinite number of sites. Let's calculate the exact result using Lieb Wu formula for a 2, 4, 6 and 8 sites and for a different potential values: 1.0, 2.8, 4.6, 6.4, 8.2, 10.0" + "### Building hamiltonians with ModelHamiltonian Package and solving the Schrödinger equation with Full CI algorithm" ] }, { "cell_type": "code", - "execution_count": 5, - "id": "82417b41", - "metadata": { - "id": "82417b41", - "outputId": "6f48c076-112e-4a8d-c8e7-df120bf78d03" - }, + "execution_count": 4, + "id": "8f87778c", + "metadata": {}, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-1.040368653394435\n", - "8.675909540485985e-11\n" - ] - }, { "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/gf/7vfqp7nn2972hrcz727tkjkh0000gn/T/ipykernel_5740/2392234220.py:8: RuntimeWarning: overflow encountered in exp\n", - " Ei, err = quad(lambda x: j0(x) * j1(x) / (x * (1 + np.exp(Ui * x / 2))),0, 200)\n" + "/opt/anaconda3/lib/python3.9/site-packages/scipy/sparse/_index.py:100: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n", + " self._set_intXint(row, col, x.flat[0])\n" ] } ], - "source": [ - "from scipy.integrate import quad\n", - "from scipy.special import *\n", - "\n", - "U = []\n", - "E_LW = []\n", - "\n", - "for Ui in np.linspace(1,10,6):\n", - " Ei, err = quad(lambda x: j0(x) * j1(x) / (x * (1 + np.exp(Ui * x / 2))),0, 200)\n", - " U.append(Ui)\n", - " E_LW.append(-4*Ei)\n", - "\n", - "print(E_LW[0])\n", - "print(err)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "f1a5654d", - "metadata": { - "id": "f1a5654d" - }, - "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -515,35 +267,30 @@ " U=[]\n", " E_tmp=[]\n", " for Ui in np.linspace(1,10,6):\n", - " ### defining the system\n", - " hubbard = HamPPP([(f\"C{i}\", f\"C{i + 1}\", 1) for i in range(1, norb)] + [(f\"C{norb}\", f\"C{1}\", 1)],\n", + " # defining the system\n", + " hubbard = HamHub([(f\"C{i}\", f\"C{i + 1}\", 1) for i in range(1, norb)] + [(f\"C{norb}\", f\"C{1}\", 1)],\n", " alpha=0, beta=-1,\n", " u_onsite=np.array([Ui for i in range(norb + 1)]))\n", " h1 = hubbard.generate_one_body_integral(basis='spatial basis', dense=True)\n", - " h2 = hubbard.generate_two_body_integral(basis='spatial basis', dense=True, sym=1)\n", + " h2 = hubbard.generate_two_body_integral(basis='spatial basis', dense=True, sym=4)\n", " \n", " ### calculating spectrum\n", - " e, fcivec = fci.direct_spin1.kernel(h1, h2, norb, nelec, nroots=10,\n", + " e, fcivec = fci.direct_spin1.kernel(h1, h2, norb, nelec, nroots=5,\n", " max_space=30, max_cycle=100)\n", " U.append(Ui)\n", " E_tmp.append(e[0])\n", - " E.append(E_tmp)\n", - " \n", - "E = np.array(E)" + " E.append(E_tmp)" ] }, { "cell_type": "code", - "execution_count": 7, - "id": "26be4bb1", - "metadata": { - "id": "26be4bb1", - "outputId": "5b832d5a-ba96-41bf-a393-35425410dbad" - }, + "execution_count": 5, + "id": "e9f96129", + "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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" ] @@ -555,7 +302,7 @@ } ], "source": [ - "# colors = ['b', 'orange', 'green']\n", + "# plotting\n", "plt.figure(dpi=150)\n", "\n", "for e, norb in zip(E, norbs):\n", @@ -570,6 +317,57 @@ "plt.title(\"Lieb-Wu Solution and FCI Solutions for Finite Systems\")\n", "plt.show();" ] + }, + { + "cell_type": "markdown", + "id": "8c5f92b3", + "metadata": {}, + "source": [ + "## Saving the output of the ModelHamiltonian Package\n", + "\n", + "Once we have generated the integrals using Model Hamiltonian, we can save the output in a file. This will allow us to use the integrals later without regenerating them.\n", + "\n", + "There are two supported file formats:\n", + "1. `.fcidump`\n", + "\n", + " In this case the integrals are saved in the FCIDUMP format. User needs to provide a TextIO file, for example `open(\"\", 'w')`, number of electron and spinpolarization. The lates is set to 0 by default.\n", + "2. `.npz file`\n", + "\n", + " In this case the integrals are saved in .npz file format. User needs to provide a filename. Energy shift, one-, and two-electron integrals are saved under the keys `e0`, `h1` and `h2` respectively.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "80867ad4", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/anaconda3/lib/python3.9/site-packages/scipy/sparse/_index.py:100: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n", + " self._set_intXint(row, col, x.flat[0])\n" + ] + } + ], + "source": [ + "# Example: generating 6 site Hubbard model\n", + "# Returning electron integrals in a spatial orbital basis\n", + "# Assuming 4-fold symmetry\n", + "norb = 4\n", + "hubbard = HamHub([(f\"C{i}\", f\"C{i + 1}\", 1) for i in range(1, norb)] + [(f\"C{norb}\", f\"C{1}\", 1)],\n", + " alpha=0, beta=-1,\n", + " u_onsite=np.array([Ui for i in range(norb + 1)]))\n", + "e0 = hubbard.generate_zero_body_integral()\n", + "h1 = hubbard.generate_one_body_integral(basis='spatial basis', dense=True)\n", + "h2 = hubbard.generate_two_body_integral(basis='spatial basis', dense=True, sym=4)\n", + " \n", + "# saving the integrals as a npz file\n", + "hubbard.savez(\"hubbard_6.npz\")\n", + "# saving the integrals as fcidump file\n", + "hubbard.save_fcidump(open('hubbard_6_site.fcidump', 'w'), nelec=6)" + ] } ], "metadata": { diff --git a/examples/Ising.ipynb b/examples/Ising.ipynb index 093c0a5..4fb308d 100644 --- a/examples/Ising.ipynb +++ b/examples/Ising.ipynb @@ -339,7 +339,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -352,7 +352,7 @@ }, { "data": { - "image/png": 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", + "image/png": 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WiYh3AecC+wJHAKtHxDe6sZk/A5tExEZlJxqHAFf3OnhJ0oBigiVJWlp8FpgSEX8BRgHfrJo/BDgwM/+Wma8DhwOLPeMkIi4G/gBsGhGzI+KTAJn5GnAs8GvgPuCyzLy3VW9GktQ/2YugJGmpkJkzgNGdzP991fSrFFe0qusd2sk6rgOu63mUkqSBzitYkiRJktQkJliSJEmS1CQmWJIkSZLUJCZYkiQtoaZMgZEjYdCg4nXKlHZHJElLPju5kCRpCTRlCowfDwsWFNOzZhXTAGPHti8uSVrSLVUJ1gMPPMDOO++8SNlBBx3E0UcfzYIFC9hzzz0XW2bcuHGMGzeOp556igMOOGCx+Z/5zGc4+OCDeeyxx/jYxz622PwvfOEL7L333jzwwAN8+tOfXmz+l7/8ZXbbbTdmzJjB8ccfv9j8b37zm+y4447ceuutfOlLX1ps/oQJExg1ahQ33ngj3/jG4o9r+fGPf8ymm27KNddcw3e+853F5k+ePJn111+fSy+9lLPPPnux+VdccQVrrrkmkyZNYtKkSYvNv+666xgyZAg/+tGPuOyyyxabP23aNADOPPNMrr322kXmrbjiilx//fUA/Pd//zc33XTTIvPXWGMNrrzySgBOPvlk/vCHPywyf8SIEVx00UUAHH/88cyYMWOR+W9/+9uZOHEiAOPHj+fBBx9cZP6oUaOYMGECAIcddhizZ89eZP4OO+zA6aefDsD+++/P/PnzF5m/66678l//9V8A7LHHHrz44ouLzB8zZgwnnHACwGLfO/C753dvAuB3r9Z3T81xyilvJlcdFiwoyk2wJKl1bCIoSdIS6NFHu1cuSWqOyMx2x9BnRo8endOnT293GJKkChFxe2bWfT6Venb+GjmyaBZYbcMNYebMpoQlSUu1eucvr2BJkrQEOu00GDJk0bIhQ4pySVLrmGBJkrQEGjsWJk4srlhFFK8TJ3r/lSS12lLVyYUkSUuTsWNNqCSpr3kFS5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5IkSZKaxARLkiRJkprEBEuSJEmSmsQES5Kkfioi9o6Iic8++2y7Q5EkNcgES5Kkfiozr8nM8cOGDWt3KJKkBplgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk7QlwYqI1SPihoh4qHxdrZO6gyPizoi4tqLs1Ih4PCJmlMOefRO5JEmSJNXXritYJwE3ZeYmwE3ldD3HAffVKP9uZo4qh+taEaQkSZIkdUe7Eqx9gQvL8QuB/WpViogRwF7AeX0TliRJkiT1XLsSrHUy8wmA8nXtOvUmACcCr9eYd2xE/CUiftJFE8PxETE9IqbPmzevt3FLkiRJUl0tS7Ai4saIuKfGsG+Dy48B5mbm7TVmnw1sDIwCngC+U289mTkxM0dn5ui11lqrB+9EkiRJkhqzTKtWnJm71ZsXEU9GxPDMfCIihgNza1TbCdin7MBiBWCViLgoMw/LzCcr1nUucG2N5SVJkiSpT7WrieDVwOHl+OHA1OoKmXlyZo7IzJHAIcDNmXkYQJmUdfgIcE9rw5UkSZKkrrUrwToD2D0iHgJ2L6eJiHUjopEeAb8dEXdHxF+AXYDPty5USZIkSWpMy5oIdiYz5wO71iifAyz2TKvMnAZMq5j+WAvDkyRJkqQeadcVLEmSJEla4phgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZIkSVKTmGBJkiRJUpOYYEmSJElSk5hgSZK6bcoUGDkSBg0qXqdMaXdEkiT1D8u0OwBJ0sAyZQqMHw8LFhTTs2YV0wBjx7YvLkmS+gOvYEmSuuWUU95MrjosWFCUq3ERsV9EnBsRUyPiQ+2OR5LUHCZYkqRuefTR7pX3JxExOCLujIhre7GOn0TE3Ii4p8a8D0fEAxHxcESc1Nl6MvOqzDwSGAcc3NN4JEn9iwmWJKlbNtige+X9zHHAfbVmRMTaETG0quxtNapOAj5cY/nBwA+BPYDNgEMjYrOI2DIirq0a1q5Y9MvlcpKkJYAJliSpW047DYYMWbRsyJCivD+LiBHAXsB5dap8AJgaESuU9Y8EvlddKTN/B/yzxvLbAQ9n5iOZ+QpwCbBvZt6dmWOqhrlR+BZwfWbe0YS3KEnqB0ywJEndMnYsTJwIG24IEcXrxIkDooOLCcCJwOu1Zmbm5cCvgEsiYizwCeCgbqx/PeCxiunZZVk9nwV2Aw6IiKNqVYiIvSNi4rPPPtuNMCRJ7WSCJUnqtrFjYeZMeP314rW/J1cRMQaYm5m3d1YvM78NvAScDeyTmc93ZzO1VtnJtr6Xmdtm5lGZeU6dOtdk5vhhw4Z1IwxJUjuZYEmSlgY7AftExEyKpnsfjIiLqitFxPuALYBfAF/t5jZmA+tXTI8A5vQoWknSgGWCJUla4mXmyZk5IjNHAocAN2fmYZV1IuJdwLnAvsARwOoR8Y1ubObPwCYRsVFELFdu5+qmvAFJ0oDR5YOGI+LtwH8CG1bWz8wPtjAuSZL62hDgwMz8G0BEHE7RhfoiIuJiYGdgzYiYDXw1M8/PzNci4ljg18Bg4CeZeW9fBS9J6h+6TLCAy4FzKP6rt7C14UiS1FqZOQ2YVqP891XTr1Kc+6rrHdrJuq8Drut1kJKkAauRBOu1zDy75ZFIkiRJ0gDXyD1Y10TE0RExPCJW7xhaHpkkSZIkDTCNXME6vHz9z4qyBN7a/HAkSZIkaeDqMsHKzI36IhBJkiRJGuga6UVwWeAzwPvLomnAj8ubfyVJkiRJpUaaCJ4NLAv8qJz+WFn2qVYFJUmSJEkDUSMJ1rszc+uK6Zsj4q5WBSRJkiRJA1UjvQgujIiNOyYi4q34PCxJkiRJWkwjV7BOAG6JiEeAADYEjmhpVJIkSZI0AHWaYEXEYGBrYBNgU4oE6/7MfLk3Gy2fo3UpMBKYCRyUmU93EsN04PHMHFNR/lngWOA14JeZeWJvYpIkSZKk3uq0iWBmLgT2ycyXM/MvmXlXb5Or0knATZm5CXBTOV3PccB9lQURsQuwL7BVZm4OnNmEmCRJkiSpVxq5B+vWiPhBRLwvIrbpGHq53X2BC8vxC4H9alWKiBHAXsB5VbM+A5zRkexl5txexiNJkiRJvdbIPVg7lq9fryhL4IO92O46mfkEQGY+ERFr16k3ATgRGFpV/nbgfRFxGvAScEJm/rnWCiJiPDAeYIMNNuhFyJIkSZLUuUYSrE9m5iOVBWVPgp2KiBuBt9SYdUojgUXEGGBuZt4eETtXzV4GWA14D/Bu4LKIeGtmZvV6MnMiMBFg9OjRi82XJEmSpGZpJMG6AqhuEng5sG1nC2XmbvXmRcSTETG8vHo1HKjVxG8nYJ+I2BNYAVglIi7KzMOA2cDPy4Tqtoh4HVgTmNfA+5EkSZKklqibYEXEO4DNgWER8dGKWatQJDy9cTVwOHBG+Tq1ukJmngycXMayM0UzwMPK2VdRNFGcFhFvB5YDnuplTJIkSZLUK51dwdoUGAOsCuxdUf4ccGQvt3sGRbO+TwKPAgcCRMS6wHmZuWcXy/8E+ElE3AO8Ahxeq3mgJEmSJPWluglWZk4FpkbEDpn5h2ZuNDPnA7vWKJ8DLJZcZeY0YFrF9CvAYdX1JEmSJKmdGumm/aiIWLVjIiJWi4iftC4kSZIkSRqYGkmwtsrMZzomMvNp4F0ti0iSJEmSBqhGEqxBEbFax0RErE5jvQ9KkiRJ0lKlkUTpO8CtEXEFxQOGDwJOa2lUkiRJkjQAdZlgZeZPI2I6RbfoAXw0M//a8sgkSZIkaYBppIkgwOrAC5n5fWBeRGzUwpgkSZIkaUDqMsGKiK8CX6R86C+wLHBRK4OSJEmSpIGokStYHwH2AV6AN55VNbSVQUmSJEnSQNRIgvVKZiZFBxdExEqtDUmSJEmSBqZGEqzLIuLHwKoRcSRwI3Bua8OSJEmSpIGnkV4Ez4yI3YF/AZsCX8nMG1oemSRJkiQNMA09MLhMqEyqJEmSJKkTdROsiHiO8r6r6llAZuYqLYtKkiRJkgaguglWZtpToCRJkiR1Q0MPGo6I90bEEeX4mj5oWJIkSZIW15MHDS+HDxqWJEmSpMX4oGFJkiRJahIfNCxJkiRJTeKDhiVJkiSpSXzQsCRJkiQ1iQ8aliRJkqQmaaibdkmSJElS10ywJEmSJKlJOk2wImJwRPjMK0mSJElqQKcJVmYuBNaKiOX6KB5JkiRJGrAa6eRiJvD7iLia8mHDAJn5v60KSpIkSZIGokYSrDnlMAgY2tpwJEmSJGngauQ5WF8DiIiVMvOFrupLkiRJ0tKqy14EI2KHiPgrcF85vXVE/KjlkUmSJEnSANNIN+0TgH8D5gNk5l3A+1sYkyRJkiQNSA09ByszH6sqWtiCWCRJkiRpQGukk4vHImJHIMvu2j9H2VxQkiRJkvSmRq5gHQUcA6wHPA6MKqcl9bEpU2DkSBg0qHidMqXdEUmSJKlSI70IPgWM7YNYJHViyhQYPx4WLCimZ80qpgHG+hcqSZLULzTSi+BbI+KaiJgXEXMjYmpEvLUvgpP0plNOeTO56rBgQVEuSZKk/qGRJoI/Ay4DhgPrApcDF7cyKEmLe/TR7pVLkiSp7zWSYEVmTs7M18rhIiBbHZikRW2wQffKJUmS1PcaSbBuiYiTImJkRGwYEScCv4yI1SNi9VYHKKlw2mkwZMiiZUOGFOWSJEnqHxrppv3g8vXTVeWfoLiS5f1YUh/o6MjilFOKZoEbbFAkV3ZwIQ1MEbEfsBewNvDDzPxNeyOSJDVDI70IbtQXgUjq2tixJlRST0TECsDvgOUpzn1XZOZXe7iunwBjgLmZuUXVvA8DZwGDgfMy84x668nMq4CrImI14EzABEuSlgCNNBGUJGmgexn4YGZuTfE8xw9HxHsqK0TE2hExtKrsbTXWNQn4cHVhRAwGfgjsAWwGHBoRm0XElhFxbdWwdsWiXy6XkyQtAUywJElLvCw8X04uWw7VHTZ9AJhaXu0iIo4EvldjXb8D/lljM9sBD2fmI5n5CnAJsG9m3p2ZY6qGuVH4FnB9Zt5RK+6I2DsiJj777LM9eduSpDYwwZIkLRUiYnBEzADmAjdk5p8q52fm5cCvgEsiYizFvcYHdWMT6wGPVUzPLsvq+SywG3BARBxVq0JmXpOZ44cNG9aNMCRJ7dTIg4avjIi9IsJkTJI0YGXmwswcBYwAtouILWrU+TbwEnA2sE/FVa9GRK3NdhLP9zJz28w8KjPP6cZ2JEn9WCNJ09nAvwMPRcQZEfGOFsckSVLLZOYzwDRq30f1PmAL4BdAdzvBmA2sXzE9ApjToyAlSQNWlwlWZt6YmWOBbYCZwA0RcWtEHBERy7Y6QEmSeisi1oqIVcvxFSma5t1fVeddwLnAvsARwOoR8Y1ubObPwCYRsVFELAccAlzdhPAlSQNIQ83+ImINYBzwKeBOii5otwFuaFlkkiQ1z3Dgloj4C0UidENmXltVZwhwYGb+LTNfBw4HZlWvKCIuBv4AbBoRsyPikwCZ+RpwLPBr4D7gssy8t2XvSJLUL3X5HKyI+DnwDmAysHdmPlHOujQiprcyOEmSmiEz/wK8q4s6v6+afpXiilZ1vUM7Wcd1wHU9DFOStAToMsECfpCZN9eakZmjmxyPJEmSJA1YjSRYq0bER6vKngXuzsy5PdloRKwOXAqMpLiv66DMfLpO3cHAdODxzBxTll0KbNoRH/BM2TOUJEmSJLVNIwnWJ4EdgFvK6Z2BPwJvj4ivZ+bkHmz3JOCmzDwjIk4qp79Yp+5xFG3ZV+koyMyDO8Yj4jsUCZ8kSZIktVUjnVy8DrwzM/fPzP2BzYCXge2pnxR1ZV/gwnL8QmC/WpUiYgSwF3BenflB8RDIi3sYhyRpAImIQRGxY7vjkCSpnkYSrJGZ+WTF9Fzg7Zn5T+DVHm53nY7OMsrXtevUmwCcSJHk1fI+4MnMfKjehiJifERMj4jp8+bN62G4kqT+oOzd7zvtjkOSpHoaaSL4/yLiWuDycnp/4HcRsRLwTL2FIuJG4C01Zp3SSGARMQaYm5m3R8TOdaodShdXrzJzIjARYPTo0dnItiVJ/dpvImJ/4OeZ6XFdktSvdJlgZebR5YnsvUAAPwWuLE9qu3Sy3G715kXEkxExPDOfiIjhFFfFqu0E7BMRewIrAKtExEWZeVi5jmWAjwLbdvUeJElLlP8AVgIWRsSLFOemzMxVOl9MkqTW6zTBiohBwF8ycwvgyiZu92qKBzieUb5Ora6QmScDJ5dx7Ayc0JFclXYD7s/M2U2MS5LUz2Xm0HbHIElSPZ3eg1W2db8rIjZo8nbPAHaPiIeA3ctpImLdiGj0AY2HYOcWkrRUioh9IuLMchjT7ngkSerQyD1Yw4F7I+I24IWOwszcp6cbzcz5wK41yucAe9YonwZMqyob19PtS5IGrog4A3g3MKUsOi4i3puZJ7UxLEmSgMYSrK+1PApJkhq3JzCqbGVBRFwI3EnxTEVJktqqkU4ufhsRGwKbZOaNETEEGNz60CRJqmtV4J/l+LA2xiFJ0iK6TLAi4khgPLA6sDGwHnAONZr4SZLUB74J3BkRt1D0IPh+yk6RJElqt0aaCB4DbAf8CSAzH4qIeg8GliSpZcrebV8H3kNxH1YAX8zMf7Q1MEmSSo0kWC9n5isRAbzx/Ckf7ChJ6nOZ+XpEHJuZl1E88kOSpH6l027aS7+NiC8BK0bE7sDlwDWtDUuSpLpuiIgTImL9iFi9Y2h3UJIkQWNXsE4CPgncDXwauA44r5VBSZLUiU+Ur8dUlCXw1jbEIknSIhrpRfB14NxykCSpbcp7sE7KzEvbHYskSbV02UQwInaKiBsi4sGIeCQi/h4Rj/RFcJIkVSr/6XdMlxUlSWqTRpoIng98HrgdWNjacCRJ6tINEXECcCnwQkdhZv6z/iKSJPWNRhKsZzPz+pZHIklSY7wHS5LUbzWSYN0SEf8D/Bx4uaMwM+9oWVSSJNWRmRu1OwZJkuppJMHavnwdXVGWwAebH44kSbVFxImZ+e1y/MDMvLxi3jcz80vti06SpEIjvQju0heBSJLUhUOAb5fjJ1M8l7HDhwETLElS2zXSi+A6EXF+RFxfTm8WEZ9sfWiSJC0i6ozXmpYkqS26TLCAScCvgXXL6QeB41sUjyRJ9WSd8VrTkiS1RSMJ1pqZeRnwOkBmvobdtUuS+t7WEfGviHgO2Koc75jest3BSZIEjXVy8UJErEH538GIeA/wbEujkiSpSmYObncMkiR1pZEE6z+Aq4GNI+L3wFrAAS2NSpIkSZIGoEZ6EbwjIj4AbEpxE/EDmflqyyOTJEmSpAGmkStYHfdd3dviWCRJkiRpQGukkwtJkiRJUgNMsCRJkiSpSRp50HBExGER8ZVyeoOI2K71oUmSJEnSwNLIFawfATsAh5bTzwE/bFlEkiRJkjRANdLJxfaZuU1E3AmQmU9HxHItjkuSJEmSBpxGrmC9GhGDefNBw2sBr7c0KkmSJEkagBpJsL4H/AJYOyJOA/4POL2lUUmSJEnSANTIg4anRMTtwK4UDxreLzPva3lkkiRJkjTAdJlgRcTkzPwYcH+NMkmSJElSqZEmgptXTpT3Y23bmnAkSZIkaeCqm2BFxMkR8RywVUT8KyKeK6fnAlP7LEJJkiQNaFOmwMiRMGhQ8TplSrsjklqnbhPBzDwdOD0iTs/Mk/swJkmSJC0hpkyB8eNhwYJietasYhpg7Nj2xSW1SpdNBDPz5IhYLSK2i4j3dwx9EZwkSZIGtlNOeTO56rBgQVEuLYka6eTiU8BxwAhgBvAe4A/AB1samSRJkga8Rx/tXrk00DXSycVxwLuBWZm5C/AuYF5Lo5IkSdISYYMNulcuDXSNJFgvZeZLABGxfGbeD2za2rAkSZK0JDjtNBgyZNGyIUOKcmlJ1EiCNTsiVgWuAm6IiKnAnFYGJUmSpCXD2LEwcSJsuCFEFK8TJ9rBhZZcXd6DlZkfKUdPjYhbgGHA9S2NSpIkSUuMsWNNqLT06PIKVkRM7hjPzN9m5tXAT1oalSRJkiQNQI00Edy8ciIiBgPbtiYcSZIkSRq46iZYEXFyRDwHbBUR/yqH54C5wNQ+i1CSJEmSBoi6CVZmnp6ZQ4H/ycxVymFoZq6RmSf3YYySJEmSNCA00kTw2ohYCSAiDouI/42IDVsclyRJkiQNOI0kWGcDCyJia+BEYBbw05ZGJUmSJEkDUCMJ1muZmcC+wFmZeRYwtLVhSZIkSdLA0+VzsIDnIuJk4DDg/WUvgsu2NixJkiRJGngauYJ1MPAy8MnM/AewHvA/LY1KkiRJkgagLq9glUnV/1ZMP4r3YEmSJEnSYhq5gtV0EbF6RNwQEQ+Vr6t1UndwRNwZEddWlI2KiD9GxIyImB4R2/VN5JIkSZJUX1sSLOAk4KbM3AS4qZyu5zjgvqqybwNfy8xRwFfKaUmSJElqq3YlWPsCF5bjFwL71aoUESOAvYDzqmYlsEo5PgyY0/wQJUmSJKl76t6DFRF3UyQyNWXmVr3Y7jqZ+US5niciYu069SZQPHurulv444FfR8SZFEnijvU2FBHjgfEAG2ywQS9CliRJkqTOddbJxZjy9ZjydXL5OhZY0NWKI+JG4C01Zp3SSGARMQaYm5m3R8TOVbM/A3w+M6+MiIOA84Hdaq0nMycCEwFGjx5dN2GUJEmSpN6qm2Bl5iyAiNgpM3eqmHVSRPwe+HpnK87MmglPuc4nI2J4efVqODC3RrWdgH0iYk9gBWCViLgoMw8DDqe4NwvgchZvQihJkiRJfa6Re7BWioj3dkxExI7ASr3c7tUUSRLl69TqCpl5cmaOyMyRwCHAzWVyBcU9Vx8oxz8IPNTLeCRJkiSp17p8DhbwSeAnETGsnH4G+EQvt3sGcFlEfBJ4FDgQICLWBc7LzD27WP5I4KyIWAZ4ifIeK0mSJElqp0YeNHw7sHVErAJEZj7b241m5nxg1xrlc4DFkqvMnAZMq5j+P2Db3sYhSZIkSc3UZYIVEcsD+wMjgWUiAoDM7PQeLEmSJEla2jTSRHAq8CxwO/Bya8ORJEmSpIGrkQRrRGZ+uOWRSJIkSdIA10gvgrdGxJYtj0SSJEmSBrhGrmC9FxgXEX+naCIYQGbmVi2NTJIkSZIGmEYSrD1aHoUkSZIkLQEaSbCy5VFIkiRJ0hKgkQTrlxRJVgArABsBDwCbtzAuSZIkSRpwGnnQ8CIdXETENsCnWxaRJEmSJA1QjfQiuIjMvAN4dwtikSRJkqQBrcsrWBHxHxWTg4BtgHkti0iSJEmSBqhG7sEaWjH+GsU9WVe2JhxJkiRJGrgauQfrawARMbSYzOdbHpUkSZIkDUBd3oMVEVtExJ3APcC9EXF7RGzR+tAkSVpyRcR+EXFuREyNiA+1Ox5JUnM00snFROA/MnPDzNwQ+EJZJknSgBAR60fELRFxX0TcGxHH9WJdP4mIuRFxT415H46IByLi4Yg4qbP1ZOZVmXkkMA44uKfxSJL6l0YSrJUy85aOicycBqzUsogkSWq+14AvZOY7gfcAx0TEZpUVImLtsjl8ZdnbaqxrEvDh6sKIGAz8ENgD2Aw4NCI2i4gtI+LaqmHtikW/XC4nSVoCNNLJxSMR8V/A5HL6MODvrQtJkqTmyswngCfK8eci4j5gPeCvFdU+AHwmIvbMzJci4kjgI8CeVev6XUSMrLGZ7YCHM/MRgIi4BNg3M08HxlRXjogAzgCuLx+BIklaAjRyBesTwFrAz8thTeCIVgYlSVKrlMnRu4A/VZZn5uXAr4BLImIsxfnvoG6sej3gsYrp2WVZPZ8FdgMOiIij6sS6d0RMfPbZZ7sRhiSpnTq9glU2d7g8M3fro3gkSWqZiFiZ4lEjx2fmv6rnZ+a3yytPZwMbd7Pn3KhRlvUqZ+b3gO91tsLMvAa4ZvTo0Ud2Iw5JUht1egUrMxcCCyJiWB/FI0lSS0TEshTJ1ZTM/HmdOu8DtgB+AXy1m5uYDaxfMT0CmNODUCVJA1gj92C9BNwdETcAL3QUZubnWhaVJElNVN7vdD5wX2b+b5067wLOBfaiuNf4ooj4RmZ+ucHN/BnYJCI2Ah4HDgH+vdfBS5IGlEYSrF+WgyRJA9VOwMco/mE4oyz7UmZeV1FnCHBgZv4NICIOp+hCfRERcTGwM7BmRMwGvpqZ52fmaxFxLPBrYDDwk8y8t0XvR5LUT3WZYGXmhX0RiCRJrZKZ/0fte6Qq6/y+avpViita1fUO7WQd1wHX1ZsvSVry1b0HKyL2jYhjKqb/FBGPlMMBfROeJEmSJA0cnXVycSJwdcX08sC7KZpFfKaFMUmSJEnSgNRZE8HlMrPyeR7/l5nzgfkRsVKL45IkSZKkAaezK1irVU5k5rEVk2u1JhxJkiRJGrg6S7D+FBGLPdgwIj4N3Na6kCRJkiRpYOqsieDngasi4t+BO8qybSnuxdqvxXFJkiRJ0oBTN8HKzLnAjhHxQWDzsviXmXlzn0QmSZIkSQNMI8/BuhkwqZIkSZKkLnR2D5YkSZIkqRtMsCRJkiSpSUywJEmSJKlJTLAkSZIkqUlMsCRJkiSpSUywJEmSJKlJTLAkSZIkqUlMsCRJkiSpSUywJEmSJKlJTLAkSZIkqUlMsCRJkiSpSUywJEmSJKlJTLAkSZIkqUlMsCRJkiSpSUywJEmSJKlJTLAkSZIkqUlMsCRJkiSpSUywJEmSJKlJ2pJgRcTqEXFDRDxUvq7WSd3BEXFnRFxbUbZ1RPwhIu6OiGsiYpW+iVySJEmS6mvXFayTgJsycxPgpnK6nuOA+6rKzgNOyswtgV8A/9mSKCVJkiSpG9qVYO0LXFiOXwjsV6tSRIwA9qJIqCptCvyuHL8B2L/5IUqSJElS97QrwVonM58AKF/XrlNvAnAi8HpV+T3APuX4gcD69TYUEeMjYnpETJ83b16vgpYkSZKkzrQswYqIGyPinhrDvg0uPwaYm5m315j9CeCYiLgdGAq8Um89mTkxM0dn5ui11lqrR+9FkiRJkhqxTKtWnJm71ZsXEU9GxPDMfCIihgNza1TbCdgnIvYEVgBWiYiLMvOwzLwf+FC5rrdTNCOUJEmSpLZqVxPBq4HDy/HDganVFTLz5MwckZkjgUOAmzPzMICIWLt8HQR8GTinL4KWJEmSpM60K8E6A9g9Ih4Cdi+niYh1I+K6BpY/NCIeBO4H5gAXtCxSSZIkSWpQy5oIdiYz5wO71iifA+xZo3waMK1i+izgrNZFKEmSJEnd164rWJIkSZK0xDHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJjHBkiRJkqQmMcGSJEmSpCYxwZIkSZKkJlmm3QFIGpheffVVZs+ezUsvvdTuUDRArLDCCowYMYJll1223aFIktQyJliSemT27NkMHTqUkSNHEhHtDkf9XGYyf/58Zs+ezUYbbdTucCRJahmbCErqkZdeeok11ljD5EoNiQjWWGMNr3hKkpZ4bUmwImL1iLghIh4qX1erU29mRNwdETMiYnp3l2+WKVNg5EgYNKh4nTKllVuTBg6TK3WH3xdJUrv1xe/6dl3BOgm4KTM3AW4qp+vZJTNHZeboHi7fK1OmwPjxMGsWZBav48ebZEmSJEkDSV/9rm9XgrUvcGE5fiGwXx8v37BTToEFCxYtW7CgKJfUHvPnz2fUqFGMGjWKt7zlLay33nqMGjWKVVddlc0226zd4b1h0qRJHHvssW3Z9jnnnMNPf/rThuuvvPLKAMyZM4cDDjigW9v6yle+wo033gjAhAkTWFB90JQkqR/oq9/17erkYp3MfAIgM5+IiLXr1EvgNxGRwI8zc2I3lycixgPjATbYYINuB/roo90rl9R6a6yxBjNmzADg1FNPZeWVV+aEE05g5syZjBkzpsfrfe2111hmmSWj75+jjjqqR8utu+66XHHFFd1a5utf//ob4xMmTOCwww5jyJAhPdq+JEmt0le/61v2SyIibgTeUmNWd3LEnTJzTplA3RAR92fm77oTR5mUTQQYPXp0dmdZgA02KC4f1iqX9Kadd955sbKDDjqIo48+mgULFrDnnnsuNn/cuHGMGzeOp556arGrJtOmTetRHAsXLuTII4/k1ltvZb311mPq1KmsuOKK/O1vf+OYY45h3rx5DBkyhHPPPZd3vOMdjBs3jtVXX50777yTbbbZhvnz57Piiity//33M2vWLC644AIuvPBC/vCHP7D99tszadIkAC6++GK++c1vkpnstddefOtb3wLgggsu4PTTT2f48OG8/e1vZ/nll+e5555jq6224sEHH2TZZZflX//6F1tttRUPPfQQu+++O9tvvz233HILzzzzDOeffz7ve9/7mDlzJh/72Md44YUXAPjBD37AjjvuyLRp0/jqV7/KOuusw4wZM/joRz/KlltuyVlnncWLL77IVVddxcYbb7xI4vnwww9z1FFHMW/ePAYPHszll1/OxhtvXHP/dSSp99xzD5MmTeKqq65i4cKF3HPPPXzhC1/glVdeYfLkySy//PJcd911rL766owbN44xY8YwZ84c5syZwy677MKaa67JLbfc0qPPUJKkVuir3/UtayKYmbtl5hY1hqnAkxExHKB8nVtnHXPK17nAL4DtylkNLd8Mp50G1f+IHTKkKJfU/zz00EMcc8wx3Hvvvay66qpceeWVAIwfP57vf//73H777Zx55pkcffTRbyzz4IMPcuONN/Kd73wHgKeffpqbb76Z7373u+y99958/vOf59577+Xuu+9mxowZzJkzhy9+8YvcfPPNzJgxgz//+c9cddVVPPHEE3z1q1/l97//PTfccAN//etfARg6dCg777wzv/zlLwG45JJL2H///d94HtRrr73GbbfdxoQJE/ja174GwNprr80NN9zAHXfcwaWXXsrnPve5N+K96667OOuss7j77ruZPHkyDz74ILfddhuf+tSn+P73v7/YPhk7dizHHHMMd911F7feeivDhw9veH/ec889/OxnP+O2227jlFNOYciQIdx5553ssMMOizVB/NznPse6667LLbfcYnIlSep3+up3fbvawlwNHA6cUb5Ora4QESsBgzLzuXL8Q8DXG12+WcaOLV5POaW4fLjBBsWH0FEuqdDZFachQ4Z0On/NNdfs8RWrahtttBGjRo0CYNttt2XmzJk8//zz3HrrrRx44IFv1Hv55ZffGD/wwAMZPHjwG9N77703EcGWW27JOuusw5ZbbgnA5ptvzsyZM5k1axY777wza621FlAkML/7XXFxvbL84IMP5sEHHwTgU5/6FN/+9rfZb7/9uOCCCzj33HPf2N5HP/rRReKF4kHOxx57LDNmzGDw4MFvrAfg3e9+9xtJ0sYbb8yHPvQhALbccsvFEpvnnnuOxx9/nI985CNA8bDf7thll10YOnQoQ4cOZdiwYey9995vbOsvf/lLt9YlSVI79dXv+nYlWGcAl0XEJ4FHgQMBImJd4LzM3BNYB/hF2a3vMsDPMvNXnS3fKmPHmlBJA8Xyyy//xvjgwYN58cUXef3111l11VXfuG+r2korrVRzHYMGDVpkfYMGDeryPq16XZHvtNNOzJw5k9/+9rcsXLiQLbbYYrHtDR48mNdeew2A7373u6yzzjrcddddvP7664skRtUxVcbbsXyHzG63jF5Ed7YlSVJ/1xe/69vSi2Bmzs/MXTNzk/L1n2X5nDK5IjMfycyty2HzzDytq+UlqZZVVlmFjTbaiMsvvxwoko677rqrx+vbfvvt+e1vf8tTTz3FwoULufjii/nABz7A9ttvz7Rp05g/fz6vvvrqG9vr8PGPf5xDDz2UI444osttPPvsswwfPpxBgwYxefJkFi5c2KNYV1llFUaMGMFVV10FFFfuWtnL39ChQ3nuuedatn5Jkvq7dnXTLkl9asqUKZx//vlsvfXWbL755kyd2vOWxcOHD+f0009nl112Yeutt2abbbZh3333Zfjw4Zx66qnssMMO7LbbbmyzzTaLLDd27FiefvppDj300C63cfTRR3PhhRfynve8hwcffHCxq2zdMXnyZL73ve+x1VZbseOOO/KPf/yjx+vqyvjx49ljjz3YZZddWrYNSZL6s+ht85GBZPTo0Tl9+vR2hyEtEe677z7e+c53tjuMAeWKK65g6tSpTJ48ud2htE2t701E3F71MHlV8fwlSf1PvfPXkvHAF0nq5z772c9y/fXXc91117U7FEmS1EImWJLUB2p1ny5JkpY83oMlqceWpibG6j2/L5KkpYEJlqQeWWGFFZg/f74/mtWQzGT+/Pndfg6XJEkDjU0EJfXIiBEjmD17NvPmzWt3KBogVlhhBUaMGNHuMCRJaikTLEk9suyyy7LRRhu1OwxJkqR+xSaCkiRJktQkJliSJEmS1CQmWJIkSZLUJLE09QAWEfOAWb1YxZrAU00Kp1WMsTn6e4z9PT4wxmbp7zE2I74NM3OtZgSzpPL81W/09xj7e3xgjM1ijL3XsvPXUpVg9VZETM/M0e2OozPG2Bz9Pcb+Hh8YY7P09xj7e3wqDITPyRh7r7/HB8bYLMbYe62MzyaCkiRJktQkJliSJEmS1CQmWN0zsd0BNMAYm6O/x9jf4wNjbJb+HmN/j0+FgfA5GWPv9ff4wBibxRh7r2XxeQ+WJEmSJDWJV7AkSZIkqUlMsCRJkiSpSUyw6oiIwRFxZ0RcW2NeRMT3IuLhiPhLRGzTz+LbOSKejYgZ5fCVvo6vjGNmRNxdxjC9xvy27scG4mv7foyIVSPiioi4PyLui4gdqub3h+9iVzG2dT9GxKYV254REf+KiOOr6rRtPzYYX3/4Ln4+Iu6NiHsi4uKIWKFqftu/iyp4/mpKjJ6/eh+j56/ex+f5qzlx9vn5a5nermAJdhxwH7BKjXl7AJuUw/bA2eVrX+osPoD/l5lj+jCeenbJzHoPcesP+7Gz+KD9+/Es4FeZeUBELAcMqZrfH/ZhVzFCG/djZj4AjILihx3wOPCLqmpt248Nxgdt3IcRsR7wOWCzzHwxIi4DDgEmVVTrD99FFTx/NYfnr97x/NVLnr96r13nL69g1RARI4C9gPPqVNkX+GkW/gisGhHD+1F8A0Vb92N/FxGrAO8HzgfIzFcy85mqau3+LjYSY3+yK/C3zJxVVd5fvov14usPlgFWjIhlKH6EzKma31/24VLN81ef8fveCc9fLeH5q+f6/PxlglXbBOBE4PU689cDHquYnl2W9ZUJdB4fwA4RcVdEXB8Rm/dNWItJ4DcRcXtEjK8xv937sav4oL378a3APOCCKJrTnBcRK1XVafc+bCRG6B/fRyj+a3VxjfJ278cO9eKDNu7DzHwcOBN4FHgCeDYzf1NVrb/sw6XdBDx/NYPnr97x/NV8nr96oF3nLxOsKhExBpibmbd3Vq1GWZ/0d99gfHcAG2bm1sD3gav6IrYadsrMbSguvR4TEe+vmt+2/VjqKr5278dlgG2AszPzXcALwElVddq9DxuJsd37EYCy+cc+wOW1Ztco69NnWHQRX1v3YUSsRvEfvo2AdYGVIuKw6mo1FvU5IH3I81dTef7qHc9fTeT5q+fadf4ywVrcTsA+ETETuAT4YERcVFVnNrB+xfQIFr/c2CpdxpeZ/8rM58vx64BlI2LNPoqvMo455etcija521VVaed+7DK+frAfZwOzM/NP5fQVFCeD6jpt24c0EGM/2I8d9gDuyMwna8xr936ETuLrB/twN+DvmTkvM18Ffg7sWFWnP+zDpZ3nrybx/NVrnr+ay/NXz7Xl/GWCVSUzT87MEZk5kuJy582ZWZ3pXg18vOx15D0Ulxuf6C/xRcRbIiLK8e0oPuf5fRFfRQwrRcTQjnHgQ8A9VdXath8bia/d+zEz/wE8FhGblkW7An+tqta2fdhojO3ejxUOpX7zhbbux1Ld+PrBPnwUeE9EDCnj2JWik4JK/WEfLtU8fzWH56/e8/zVdJ6/eq4t5y97EWxQRBwFkJnnANcBewIPAwuAI9oYGrBYfAcAn4mI14AXgUMys6+b6qwD/KL8m1oG+Flm/qof7cdG4usP+/GzwJQoLr8/AhzRj/ZhozG2fT9GxBBgd+DTFWX9Zj82EF9b92Fm/ikirqBo6vEacCcwsT/tQ9XX3z+n/vRdL3n+ag7PX03g+at32nX+ir7/e5MkSZKkJZNNBCVJkiSpSUywJEmSJKlJTLAkSZIkqUlMsCRJkiSpSUywJEmSJKlJTLCkJoiIUyLi3oj4S0TMiIjte7COcRGxbiviq7O9r0fEbn21PUlS/+K5S2oNn4Ml9VJE7ACMAbbJzJejeEL5cj1Y1TiKh0X2yRPYM/MrfbEdSVL/47lLah2vYEm9Nxx4KjNfBsjMpzJzTkTsGhG/6KgUEbtHxM8jYnBETIqIeyLi7oj4fEQcAIymeODhjIhYMSK2jYjfRsTtEfHriBhermdaRHw3In4XEfdFxLvL9T4UEd+oDq7W9srySRFxQESMLrc5o5yf5fyNI+JX5fb/X0S8ow/2pSSpb3juklrEK1hS7/0G+EpEPAjcCFyamb8FbgZ+GBFrZeY8iieDXwCMAtbLzC0AImLVzHwmIo4FTsjM6RGxLPB9YN/MnBcRBwOnAZ8ot/lKZr4/Io4DpgLbAv8E/hYR383M+RXxLba9yuAzc3pZh4j4H+BX5ayJwFGZ+VDZbORHwAebsL8kSe3nuUtqERMsqZcy8/mI2BZ4H7ALcGlEnJSZkyJiMnBYRFwA7AB8HBgKvDUivg/8kuIkV21TYAvghogAGAw8UTH/6vL1buDezHwCICIeAdYHKk9SjzSwPSLiIGAb4EMRsTKwI3B5uX2A5RvcJZKkfs5zl9Q6JlhSE2TmQmAaMC0i7gYOByZR/NfvGuAl4PLMfA14OiK2Bv4NOAY4iDf/u9chKE4+O9TZ5Mvl6+sV4x3Ti/xdZ2aX24uIzYGvAe/PzIURMQh4JjNHNfL+JUkDj+cuqTW8B0vqpYjYNCI2qSgaBcwCyMw5FDf+fpnipEUUNxIPyswrgf+i+M8bwHMU/yEEeABYK4qbkImIZcsTSU/iq7e9jvnDgEuAj5fNQcjMfwF/j4gDyzpRnugkSUsAz11S63gFS+q9lYHvl+3DXwMeBsZXzJ8CrJWZfy2n1wMuKP/TBnBy+ToJOCciXqRoknEA8L3yJLIMMAG4twfx1dteh/2ADYFzO5pUlP/9GwucHRFfBpalOJHd1YPtS5L6H89dUotEZrY7BmmJFhE/AO7MzPPbHYskSY3w3CX1nAmW1EIRcTvwArB7R1e4kiT1Z567pN4xwZIkSZKkJrGTC0mSJElqEhMsSZIkSWoSEyxJkiRJahITLEmSJElqEhMsSZIkSWqS/w8ugPRIiD4gwQAAAABJRU5ErkJggg==", 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" ] @@ -412,6 +412,50 @@ "plt.tight_layout()\n", "plt.show()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Saving the output of the ModelHamiltonian Package\n", + "\n", + "Once we have generated the integrals using Model Hamiltonian, we can save the output in a file. This will allow us to use the integrals later without regenerating them.\n", + "\n", + "There are two supported file formats:\n", + "1. `.fcidump`\n", + "\n", + " In this case the integrals are saved in the FCIDUMP format. User needs to provide a TextIO file, for example `open(\"\", 'w')`, number of electron and spinpolarization. The lates is set to 0 by default.\n", + "2. `.npz file`\n", + "\n", + " In this case the integrals are saved in .npz file format. User needs to provide a filename. Energy shift, one-, and two-electron integrals are saved under the keys `e0`, `h1` and `h2` respectively.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Constructing the XXZ Hamiltonian using the HamHeisenberg class\n", + "\n", + "# Define the Hamiltonian parameters\n", + "L = 4\n", + "connectivity = np.zeros((L, L))\n", + "connectivity[np.arange(L-1), np.arange(L-1)+1] = 1\n", + "connectivity[0, -1] = 1\n", + "connectivity += connectivity.T\n", + "\n", + "# Define the Hamiltonian\n", + "ham = HamHeisenberg(connectivity=connectivity, J_eq=1, J_ax=0.2, mu=0)\n", + "e0 = ham.generate_zero_body_integral()\n", + "h1 = ham.generate_one_body_integral(dense=True, basis='spatial basis')\n", + "h2 = ham.generate_two_body_integral(dense=True, basis='spatial basis', sym=4)\n", + "\n", + "# save the Hamiltonian to npz file\n", + "ham.savez('Heisenberg_4_site.npz')\n", + "# save the Hamiltonian to fcidump file\n", + "ham.save_fcidump(open('Heisenberg_4_site.fcidump', 'w'), L, 0)" + ] } ], "metadata": { From b1dcbc89d6b4b1495a0daf0ffbbf748e20312131 Mon Sep 17 00:00:00 2001 From: = Date: Thu, 11 Apr 2024 16:12:56 -0400 Subject: [PATCH 4/4] fix pycodestyle --- moha/api.py | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/moha/api.py b/moha/api.py index 5abc6d0..f1a3fe0 100644 --- a/moha/api.py +++ b/moha/api.py @@ -369,12 +369,12 @@ def save_triqs(self, fname: str, integral): def savez(self, fname: str): r"""Save file as regular npz file. - + Parameters ---------- fname: str name of the file - + Returns ------- None @@ -397,7 +397,6 @@ def savez(self, fname: str): np.savez(fname, e0=e0, h1=h, h2=v) - def expand_sym(sym, integral, nbody): r""" Restore permutational symmetry of one- and two-body terms.