3 site tests (#180)

* Added some tests for a 3-site unit cell

* formatting...

* Added some more tests for vumpssvd. This will be helpfull when we paralelize it !

* formatted

* changed order of tests according to @lukas

* now also mentions current unit_cell_size

* Now tests re-use prior converged states

* fixed groundstate-alg part of tests

* formatting

* small formatting changes

* reenable test

---------

Co-authored-by: lkdvos <[email protected]>
Co-authored-by: Lukas Devos <[email protected]>

Author: Gertian

test/algorithms.jl

@@ -72,14 +72,17 @@ end
     tol = 1e-8
     g = 4.0
     D = 6
-    H = force_planar(transverse_field_ising(; g))
 
-    @testset "VUMPS" begin
-        ψ₀ = InfiniteMPS(ℙ^2, ℙ^D)
-        v₀ = variance(ψ₀, H)
+    H_ref = force_planar(transverse_field_ising(; g))
+    ψ = InfiniteMPS(ℙ^2, ℙ^D)
+    v₀ = variance(ψ, H_ref)
+
+    @testset "VUMPS" for unit_cell_size in [1, 3]
+        ψ = unit_cell_size == 1 ? InfiniteMPS(ℙ^2, ℙ^D) : repeat(ψ, unit_cell_size)
+        H = repeat(H_ref, unit_cell_size)
 
         # test logging
-        ψ, envs, δ = find_groundstate(ψ₀, H, VUMPS(; tol, verbosity=5, maxiter=2))
+        ψ, envs, δ = find_groundstate(ψ, H, VUMPS(; tol, verbosity=5, maxiter=2))
 
         ψ, envs, δ = find_groundstate(ψ, H, VUMPS(; tol, verbosity=1))
         v = variance(ψ, H, envs)
@@ -90,12 +93,12 @@ end
         @test v < 1e-2
     end
 
-    @testset "IDMRG1" begin
-        ψ₀ = InfiniteMPS(ℙ^2, ℙ^D)
-        v₀ = variance(ψ₀, H)
+    @testset "IDMRG1" for unit_cell_size in [1, 3]
+        ψ = unit_cell_size == 1 ? InfiniteMPS(ℙ^2, ℙ^D) : repeat(ψ, unit_cell_size)
+        H = repeat(H_ref, unit_cell_size)
 
         # test logging
-        ψ, envs, δ = find_groundstate(ψ₀, H, IDMRG1(; tol, verbosity=5, maxiter=2))
+        ψ, envs, δ = find_groundstate(ψ, H, IDMRG1(; tol, verbosity=5, maxiter=2))
 
         ψ, envs, δ = find_groundstate(ψ, H, IDMRG1(; tol, verbosity=1))
         v = variance(ψ, H, envs)
@@ -107,32 +110,32 @@ end
     end
 
     @testset "IDMRG2" begin
-        ψ₀ = repeat(InfiniteMPS(ℙ^2, ℙ^D), 2)
-        H2 = repeat(H, 2)
-        v₀ = variance(ψ₀, H2)
+        ψ = repeat(InfiniteMPS(ℙ^2, ℙ^D), 2)
+        H = repeat(H_ref, 2)
+
         trscheme = truncbelow(1e-8)
 
         # test logging
-        ψ, envs, δ = find_groundstate(ψ₀, H2,
+        ψ, envs, δ = find_groundstate(ψ, H,
                                       IDMRG2(; tol, verbosity=5, maxiter=2,
                                              trscheme))
 
-        ψ, envs, δ = find_groundstate(ψ, H2,
+        ψ, envs, δ = find_groundstate(ψ, H,
                                       IDMRG2(; tol, verbosity=1, trscheme))
-        v = variance(ψ, H2, envs)
+        v = variance(ψ, H, envs)
 
         # test using low variance
         @test sum(δ) ≈ 0 atol = 1e-3
         @test v < v₀
         @test v < 1e-2
     end
 
-    @testset "GradientGrassmann" begin
-        ψ₀ = InfiniteMPS(ℙ^2, ℙ^D)
-        v₀ = variance(ψ₀, H)
+    @testset "GradientGrassmann" for unit_cell_size in [1, 3]
+        ψ = unit_cell_size == 1 ? InfiniteMPS(ℙ^2, ℙ^D) : repeat(ψ, unit_cell_size)
+        H = repeat(H_ref, unit_cell_size)
 
         # test logging
-        ψ, envs, δ = find_groundstate(ψ₀, H,
+        ψ, envs, δ = find_groundstate(ψ, H,
                                       GradientGrassmann(; tol, verbosity=5, maxiter=2))
 
         ψ, envs, δ = find_groundstate(ψ, H, GradientGrassmann(; tol, verbosity=1))
@@ -144,13 +147,13 @@ end
         @test v < 1e-2
     end
 
-    @testset "Combination" begin
-        ψ₀ = InfiniteMPS(ℙ^2, ℙ^D)
-        v₀ = variance(ψ₀, H)
+    @testset "Combination" for unit_cell_size in [1, 3]
+        ψ = unit_cell_size == 1 ? InfiniteMPS(ℙ^2, ℙ^D) : repeat(ψ, unit_cell_size)
+        H = repeat(H_ref, unit_cell_size)
 
         alg = VUMPS(; tol=100 * tol, verbosity=1, maxiter=10) &
               GradientGrassmann(; tol, verbosity=1, maxiter=50)
-        ψ, envs, δ = find_groundstate(ψ₀, H, alg)
+        ψ, envs, δ = find_groundstate(ψ, H, alg)
 
         v = variance(ψ, H, envs)
 
@@ -452,7 +455,7 @@ end
                                                                Rep[SU₂](0 => 2, 1 => 2,
                                                                         2 => 1))]
     @testset "mpo" begin
-        #random nn interaction
+        # random nn interaction
         nn = TensorMap(rand, ComplexF64, pspace * pspace, pspace * pspace)
         nn += nn'
         H = MPOHamiltonian(nn)
@@ -467,33 +470,49 @@ end
     end
 
     @testset "infinite mps" begin
-        #random nn interaction
+        # random nn interaction
         nn = TensorMap(rand, ComplexF64, pspace * pspace, pspace * pspace)
         nn += nn'
 
-        state = InfiniteMPS([pspace, pspace], [Dspace, Dspace])
-
-        state_re = changebonds(state,
-                               RandExpand(; trscheme=truncdim(dim(Dspace) * dim(Dspace))))
-        @test dot(state, state_re) ≈ 1 atol = 1e-8
-
-        state_oe, _ = changebonds(state,
-                                  repeat(MPOHamiltonian(nn), 2),
-                                  OptimalExpand(;
-                                                trscheme=truncdim(dim(Dspace) *
-                                                                  dim(Dspace))))
-        @test dot(state, state_oe) ≈ 1 atol = 1e-8
-
-        state_vs, _ = changebonds(state, repeat(MPOHamiltonian(nn), 2),
-                                  VUMPSSvdCut(; trscheme=notrunc()))
-        @test dim(left_virtualspace(state, 1)) < dim(left_virtualspace(state_vs, 1))
+        # test rand_expand
+        for unit_cell_size in 2:3
+            H = repeat(MPOHamiltonian(nn), unit_cell_size)
+            state = InfiniteMPS(fill(pspace, unit_cell_size), fill(Dspace, unit_cell_size))
 
-        state_vs_tr = changebonds(state_vs, SvdCut(; trscheme=truncdim(dim(Dspace))))
-        @test dim(right_virtualspace(state_vs_tr, 1)) < dim(right_virtualspace(state_vs, 1))
+            state_re = changebonds(state,
+                                   RandExpand(;
+                                              trscheme=truncdim(dim(Dspace) * dim(Dspace))))
+            @test dot(state, state_re) ≈ 1 atol = 1e-8
+        end
+        # test optimal_expand
+        for unit_cell_size in 2:3
+            H = repeat(MPOHamiltonian(nn), unit_cell_size)
+            state = InfiniteMPS(fill(pspace, unit_cell_size), fill(Dspace, unit_cell_size))
+
+            state_oe, _ = changebonds(state,
+                                      H,
+                                      OptimalExpand(;
+                                                    trscheme=truncdim(dim(Dspace) *
+                                                                      dim(Dspace))))
+            @test dot(state, state_oe) ≈ 1 atol = 1e-8
+        end
+        # test VUMPSSvdCut
+        for unit_cell_size in [1, 2, 3, 4]
+            H = repeat(MPOHamiltonian(nn), unit_cell_size)
+            state = InfiniteMPS(fill(pspace, unit_cell_size), fill(Dspace, unit_cell_size))
+
+            state_vs, _ = changebonds(state, H,
+                                      VUMPSSvdCut(; trscheme=notrunc()))
+            @test dim(left_virtualspace(state, 1)) < dim(left_virtualspace(state_vs, 1))
+
+            state_vs_tr = changebonds(state_vs, SvdCut(; trscheme=truncdim(dim(Dspace))))
+            @test dim(right_virtualspace(state_vs_tr, 1)) <
+                  dim(right_virtualspace(state_vs, 1))
+        end
     end
 
     @testset "finite mps" begin
-        #random nn interaction
+        # random nn interaction
         nn = TensorMap(rand, ComplexF64, pspace * pspace, pspace * pspace)
         nn += nn'
 
@@ -576,15 +595,15 @@ end
     for λ in [1.05, 2.0, 4.0]
         H = hamiltonian(λ)
         ψ = InfiniteMPS([ℂ^2], [ℂ^16])
-        ψ, envs, = find_groundstate(ψ, H, VUMPS(; maxiter=100, verbosity=0))
+        ψ, envs = find_groundstate(ψ, H, VUMPS(; maxiter=100, verbosity=0))
 
         numerical_scusceptibility = fidelity_susceptibility(ψ, H, [H_X], envs; maxiter=10)
         @test numerical_scusceptibility[1, 1] ≈ analytical_susceptibility(λ) atol = 1e-2
 
         # test if the finite fid sus approximates the analytical one with increasing system size
         fin_en = map([20, 15, 10]) do L
             ψ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^16)
-            ψ, envs, = find_groundstate(ψ, H, DMRG(; verbosity=0))
+            ψ, envs = find_groundstate(ψ, H, DMRG(; verbosity=0))
             numerical_scusceptibility = fidelity_susceptibility(ψ, H, [H_X], envs;
                                                                 maxiter=10)
             return numerical_scusceptibility[1, 1] / L
@@ -593,7 +612,7 @@ end
     end
 end
 
-#stub tests
+# stub tests
 @testset "correlation length / entropy" begin
     ψ = InfiniteMPS([ℙ^2], [ℙ^10])
     H = force_planar(transverse_field_ising())
@@ -697,20 +716,20 @@ end
 @testset "periodic boundary conditions" begin
     len = 10
 
-    #impose periodic boundary conditions on the hamiltonian (circle size 10)
+    # impose periodic boundary conditions on the hamiltonian (circle size 10)
     H = transverse_field_ising()
     H = periodic_boundary_conditions(H, len)
 
     ψ = FiniteMPS(len, ℂ^2, ℂ^10)
 
     gs, envs = find_groundstate(ψ, H, DMRG(; verbosity=0))
 
-    #translation mpo:
+    # translation mpo:
     @tensor bulk[-1 -2; -3 -4] := isomorphism(ℂ^2, ℂ^2)[-2, -4] *
                                   isomorphism(ℂ^2, ℂ^2)[-1, -3]
     translation = periodic_boundary_conditions(DenseMPO(bulk), len)
 
-    #the groundstate should be translation invariant:
+    # the groundstate should be translation invariant:
     ut = Tensor(ones, ℂ^1)
     @tensor leftstart[-1 -2; -3] := l_LL(gs)[-1, -3] * conj(ut[-2])
     T = TransferMatrix([gs.AC[1]; gs.AR[2:end]], translation[:], [gs.AC[1]; gs.AR[2:end]])