improve WII coverage and fix

Author: lkdvos

src/algorithms/timestep/wii.jl

@@ -28,7 +28,8 @@ function make_time_mpo(
     WC = H.C
     WD = H.D
 
-    δ = imaginary_evolution ? -dt : (-1im * dt)
+    # needs to be complex if negative because of square root
+    δ = imaginary_evolution ? -complex(dt) : (-1im * dt)
     exp_alg = Arnoldi(; alg.tol, alg.maxiter)
 
     Wnew = map(1:length(H)) do i
@@ -109,9 +110,9 @@ function make_time_mpo(
     H′[1][end, 1, 1, end] = H′[1][1, 1, 1, 1]
     H′[end][1, 1, 1, 1] = H′[end][end, 1, 1, end]
 
-    mpo = make_time_mpo(InfiniteMPOHamiltonian(H′), dt, alg; tol, imaginary_evolution)
+    mpo = make_time_mpo(InfiniteMPOHamiltonian(H′), dt, alg; imaginary_evolution)
 
     # Impose boundary conditions
     mpo_fin = open_boundary_conditions(mpo, length(H))
-    return remove_orphans!(mpo_fin; tol)
+    return remove_orphans!(mpo_fin; alg.tol)
 end

test/algorithms.jl

@@ -971,6 +971,13 @@ module TestAlgorithms
         E_x_taylor = @constinferred expectation_value(rho_taylor_1, 1 => S_x())
         E_xx_taylor = @constinferred expectation_value(rho_taylor_1, (1, 2) => S_xx())
 
+        # WII
+        rho_wii = make_time_mpo(H, beta, WII(); imaginary_evolution = true)
+        Z_wii = tr(rho_wii)^(1 / L)
+        @test Z_wii ≈ Z_dense_1 atol = 1.0e-2
+        @test expectation_value(rho_wii, 1 => S_x()) ≈ E_x_taylor atol = 1.0e-2
+        @test expectation_value(rho_wii, (1, 2) => S_xx()) ≈ E_xx_taylor atol = 1.0e-2
+
         # MPO multiplication
         rho_mps = convert(FiniteMPS, rho_taylor_1)
         rho_mps, = approximate(rho_mps, (rho_taylor_1, rho_mps), DMRG2(; trscheme, verbosity))