diff --git a/src/algorithms/statmech/vumps.jl b/src/algorithms/statmech/vumps.jl
index 26bdffb2c..5d1b4daec 100644
--- a/src/algorithms/statmech/vumps.jl
+++ b/src/algorithms/statmech/vumps.jl
@@ -3,70 +3,82 @@
 # - leading_boundary primarily works on MPSMultiline
 # - they search for different eigenvalues
 # - ham vumps should use Lanczos, this has to use arnoldi
-# - this vumps updates entire collumns (state[:,i]); incompatible with InfiniteMPS
+# - this vumps updates entire collumns (Ψ[:,i]); incompatible with InfiniteMPS
 # - (a)c-prime takes a different number of arguments
 # - it's very litle duplicate code, but together it'd be a bit more convoluted (primarily because of the indexing way)
 
 "
-    leading_boundary(state,opp,alg,envs=environments(state,ham))
+    leading_boundary(Ψ,opp,alg,envs=environments(Ψ,ham))
 
     approximate the leading eigenvector for opp
 "
-function leading_boundary(state::InfiniteMPS, H, alg, envs=environments(state, H))
-    (st, pr, de) = leading_boundary(convert(MPSMultiline, state), Multiline([H]), alg, envs)
+function leading_boundary(Ψ::InfiniteMPS, H, alg, envs=environments(Ψ, H))
+    (st, pr, de) = leading_boundary(convert(MPSMultiline, Ψ), Multiline([H]), alg, envs)
     return convert(InfiniteMPS, st), pr, de
 end
 
-function leading_boundary(state::MPSMultiline, H, alg::VUMPS, envs=environments(state, H))
+function leading_boundary(Ψ::MPSMultiline, H, alg::VUMPS, envs=environments(Ψ, H))
     galerkin = 1 + alg.tol_galerkin
     iter = 1
 
-    temp_ACs = similar.(state.AC)
-    temp_Cs = similar.(state.CR)
+    temp_ACs = similar.(Ψ.AC)
+    temp_Cs = similar.(Ψ.CR)
 
     while true
-        eigalg = Arnoldi(; tol=alg.tol_galerkin / 10)
-
-        @sync for col in 1:size(state, 2)
-            Threads.@spawn begin
-                H_AC = ∂∂AC($col, $state, $H, $envs)
-
-                (vals_ac, vecs_ac) = eigsolve(
-                    H_AC, RecursiveVec($state.AC[:, col]), 1, :LM, eigalg
-                )
-                $temp_ACs[:, col] = vecs_ac[1].vecs[:]
+        eigalg = Arnoldi(; tol=galerkin / (4 * sqrt(iter)))
+        
+        if Defaults.parallelize_sites
+            @sync begin
+                for col in 1:size(Ψ, 2)
+                    Threads.@spawn begin
+                        H_AC = ∂∂AC($col, $Ψ, $H, $envs)
+                        ac = RecursiveVec($Ψ.AC[:, col])
+                        _, acvecs = eigsolve(H_AC, ac, 1, :LM, eigalg)
+                        $temp_ACs[:, col] = acvecs[1].vecs[:]
+                    end
+                    
+                    Threads.@spawn begin
+                        H_C = ∂∂C($col, $Ψ, $H, $envs)
+                        c = RecursiveVec($Ψ.CR[:, col])
+                        _, cvecs = eigsolve(H_C, c, 1, :LM, eigalg)
+                        $temp_Cs[:, col] = cvecs[1].vecs[:]
+                    end
+                end
             end
-
-            Threads.@spawn begin
-                H_C = ∂∂C($col, $state, $H, $envs)
-
-                (vals_c, vecs_c) = eigsolve(
-                    H_C, RecursiveVec($state.CR[:, col]), 1, :LM, eigalg
-                )
-                $temp_Cs[:, col] = vecs_c[1].vecs[:]
+        else
+            for col in 1:size(Ψ, 2)
+                H_AC = ∂∂AC(col, Ψ, H, envs)
+                ac = RecursiveVec(Ψ.AC[:, col])
+                _, acvecs = eigsolve(H_AC, ac, 1, :LM, eigalg)
+                temp_ACs[:, col] = acvecs[1].vecs[:]
+                
+                H_C = ∂∂C(col, Ψ, H, envs)
+                c = RecursiveVec(Ψ.CR[:, col])
+                _, cvecs = eigsolve(H_C, c, 1, :LM, eigalg)
+                temp_Cs[:, col] = cvecs[1].vecs[:]
             end
         end
 
-        for row in 1:size(state, 1), col in 1:size(state, 2)
+        for row in 1:size(Ψ, 1), col in 1:size(Ψ, 2)
             QAc, _ = leftorth!(temp_ACs[row, col]; alg=TensorKit.QRpos())
             Qc, _ = leftorth!(temp_Cs[row, col]; alg=TensorKit.QRpos())
             temp_ACs[row, col] = QAc * adjoint(Qc)
         end
 
-        state = MPSMultiline(
-            temp_ACs, state.CR[:, end]; tol=alg.tol_gauge, maxiter=alg.orthmaxiter
+        Ψ = MPSMultiline(
+            temp_ACs, Ψ.CR[:, end]; tol=alg.tol_gauge, maxiter=alg.orthmaxiter
         )
-        recalculate!(envs, state)
+        recalculate!(envs, Ψ)
 
-        (state, envs) =
-            alg.finalize(iter, state, H, envs)::Tuple{typeof(state),typeof(envs)}
+        (Ψ, envs) =
+            alg.finalize(iter, Ψ, H, envs)::Tuple{typeof(Ψ),typeof(envs)}
 
-        galerkin = calc_galerkin(state, envs)
+        galerkin = calc_galerkin(Ψ, envs)
         alg.verbose && @info "vumps @iteration $(iter) galerkin = $(galerkin)"
 
         if (galerkin <= alg.tol_galerkin) || iter >= alg.maxiter
             iter >= alg.maxiter && @warn "vumps didn't converge $(galerkin)"
-            return state, envs, galerkin
+            return Ψ, envs, galerkin
         end
 
         iter += 1