MPSKitModels.jl/test/ashkin_teller.jl at 563690930e7b7828cffd5ad82b9f990f11b5d2cf · QuantumKitHub/MPSKitModels.jl · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
using Test
using TensorKit
using MPSKit
using MPSKitModels

# Setup

gammas = [
    pi / 2, pi / 3, pi / 4, pi / 6, 0,
]
# Exact GS energy density via mapping to spin 1/2 XXZ and Bethe ansatz
# https://www.sciencedirect.com/science/article/pii/0003491688900152
E0s = [
    -8 / pi, -12 / 4, -4 * (sqrt(2) / pi + 1 / (2 * sqrt(2))),
    -4 * (1 / pi + 11 / (12 * sqrt(3))), 2 - 8 * log(2),
]
alg = VUMPS(; maxiter = 100, verbosity = 0)

S = Z2Irrep ⊠ Z2Irrep
V = Vect[S](c => 1 for c in values(S))
W = Vect[S](c => 6 for c in values(S))

# Test

@testset "Ashkin-Teller" for (gamma, E0) in zip(gammas, E0s)

    H = ashkin_teller(h = 1, J = 1, λ = cos(gamma))
    Ψ = InfiniteMPS(V, W)

    @test imag(expectation_value(Ψ, H)) ≈ 0 atol = 1.0e-12

    Ψ0, _ = find_groundstate(Ψ, H, alg)
    @test real(expectation_value(Ψ0, H)) ≈ E0 atol = 1.0e-3
end