Fix time dependent integral of TDVP and TDVP2 (#279)

* try fix

* try fix

* format documents

Author: GiggleLiu

src/algorithms/timestep/tdvp.jl

@@ -78,7 +78,7 @@ function timestep!(ψ::AbstractFiniteMPS, H, t::Number, dt::Number, alg::TDVP,
         ψ.AC[i] = integrate(h_ac, ψ.AC[i], t, dt / 2, alg.integrator)
 
         h_c = ∂∂C(i, ψ, H, envs)
-        ψ.C[i] = integrate(h_c, ψ.C[i], t, -dt / 2, alg.integrator)
+        ψ.C[i] = integrate(h_c, ψ.C[i], t + dt / 2, -dt / 2, alg.integrator)
     end
 
     # edge case
@@ -91,7 +91,7 @@ function timestep!(ψ::AbstractFiniteMPS, H, t::Number, dt::Number, alg::TDVP,
         ψ.AC[i] = integrate(h_ac, ψ.AC[i], t + dt / 2, dt / 2, alg.integrator)
 
         h_c = ∂∂C(i - 1, ψ, H, envs)
-        ψ.C[i - 1] = integrate(h_c, ψ.C[i - 1], t + dt / 2, -dt / 2, alg.integrator)
+        ψ.C[i - 1] = integrate(h_c, ψ.C[i - 1], t + dt, -dt / 2, alg.integrator)
     end
 
     # edge case
@@ -148,7 +148,8 @@ function timestep!(ψ::AbstractFiniteMPS, H, t::Number, dt::Number, alg::TDVP2,
         ψ.AC[i + 1] = (complex(nc), _transpose_front(nar))
 
         if i != (length(ψ) - 1)
-            ψ.AC[i + 1] = integrate(∂∂AC(i + 1, ψ, H, envs), ψ.AC[i + 1], t, -dt / 2,
+            ψ.AC[i + 1] = integrate(∂∂AC(i + 1, ψ, H, envs), ψ.AC[i + 1], t + dt / 2,
+                                    -dt / 2,
                                     alg.integrator)
         end
     end
@@ -164,7 +165,7 @@ function timestep!(ψ::AbstractFiniteMPS, H, t::Number, dt::Number, alg::TDVP2,
         ψ.AC[i] = (complex(nc), _transpose_front(nar))
 
         if i != 2
-            ψ.AC[i - 1] = integrate(∂∂AC(i - 1, ψ, H, envs), ψ.AC[i - 1], t + dt / 2,
+            ψ.AC[i - 1] = integrate(∂∂AC(i - 1, ψ, H, envs), ψ.AC[i - 1], t + dt,
                                     -dt / 2, alg.integrator)
         end
     end

test/algorithms.jl

@@ -356,6 +356,18 @@ end
         @test E ≈ Et atol = 1e-8
     end
 
+    Ht2 = MultipliedOperator(H, t -> t < 0 ? error("t < 0!") : 4) +
+          MultipliedOperator(H, 1.45)
+    @testset "Finite TimeDependent LazySum (fix negative t issue) $(alg isa TDVP ? "TDVP" : "TDVP2")" for alg in
+                                                                                                          algs
+        ψ, envs = timestep(ψ₀, Ht2, 0.0, dt, alg)
+        E = expectation_value(ψ, Ht2(0.0), envs)
+
+        ψt, envst = timestep(ψ₀, Ht2, 0.0, dt, alg)
+        Et = expectation_value(ψt, Ht2(0.0), envst)
+        @test E ≈ Et atol = 1e-8
+    end
+
     H = repeat(force_planar(heisenberg_XXX(; spin=1)), 2)
     ψ₀ = InfiniteMPS([ℙ^3, ℙ^3], [ℙ^50, ℙ^50])
     E₀ = expectation_value(ψ₀, H)