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using SpinGlassPEPS | ||
using MetaGraphs | ||
using LightGraphs | ||
using Test | ||
using TensorCast | ||
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function make_particular_tensors(D) | ||
h1 = D[(1,1)] | ||
h2 = D[(2,2)] | ||
J12 = D[(1,2)] | ||
J23 = D[(2,3)] | ||
h3 = D[(3,3)] | ||
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if D[(1, 2)] == 0.652 | ||
A1ex = reshape([exp(h1+h2-J12) 0. exp(-h1+h2+J12) 0.; 0. exp(h1-h2+J12) 0. exp(-h1-h2-J12)], (1,1,2,1,4)) | ||
A2ex = reshape([exp(h3-J23) exp(-h3+J23); exp(h3+J23) exp(-h3-J23)],(2,1,1,1,2)) | ||
C = [exp(h1+h2-J12+h3-J23) exp(h1-h2+J12+h3+J23) exp(-h1+h2+J12+h3-J23) exp(-h1-h2-J12+h3+J23); exp(h1+h2-J12-h3+J23) exp(h1-h2+J12-h3-J23) exp(-h1+h2+J12-h3+J23) exp(-h1-h2-J12-h3-J23)] | ||
else | ||
A1ex = reshape([exp(-h1-h2-J12) 0. 0. exp(h1-h2+J12); 0. exp(h1+h2-J12) exp(-h1+h2+J12) 0.], (1,1,2,1,4)) | ||
A2ex = reshape([exp(-h3-J23) exp(h3+J23); exp(-h3+J23) exp(h3-J23)],(2,1,1,1,2)) | ||
C = [exp(-h1-h2-J12-h3-J23) exp(h1+h2-J12-h3+J23) exp(-h1+h2+J12-h3+J23) exp(h1-h2+J12-h3-J23); exp(-h1-h2-J12+h3+J23) exp(h1+h2-J12+h3-J23) exp(-h1+h2+J12+h3-J23) exp(h1-h2+J12+h3+J23)] | ||
end | ||
A1ex, A2ex, C | ||
end | ||
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function show_dificult_example(C, fg) | ||
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println("states of T1 ", get_prop(fg, 1, :spectrum).states) | ||
println("x") | ||
println("states of T2 ", get_prop(fg, 2, :spectrum).states) | ||
println("D2, tensor with beta = 1") | ||
display(C) | ||
println() | ||
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println("D2, tensor with beta = $β") | ||
display(C.^β) | ||
println() | ||
end | ||
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@testset "Test if the solution of the tensor agreeds with the BF" begin | ||
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# grid | ||
# A1 | A2 | ||
# | | ||
# 1 -- 2 -|- 3 | ||
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D1 = Dict((1, 2) => 0.652,(2, 3) => 0.73,(3, 3) => 0.592,(2, 2) => 0.704,(1, 1) => 0.868) | ||
D2 = Dict((1, 2) => -0.9049,(2, 3) => 0.2838,(3, 3) => -0.7928,(2, 2) => 0.1208,(1, 1) => -0.3342) | ||
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for D in [D1, D2] | ||
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m = 1 | ||
n = 2 | ||
t = 2 | ||
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L = m * n * t | ||
g_ising = ising_graph(D, L) | ||
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# brute force solution | ||
bf = brute_force(g_ising; num_states = 1) | ||
states = bf.states[1] | ||
sol_A1 = states[[1,2]] | ||
sol_A2 = states[[3]] | ||
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#particular form of peps tensors | ||
update_cells!( | ||
g_ising, | ||
rule = square_lattice((m, 1, n, 1, t)), | ||
) | ||
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fg = factor_graph( | ||
g_ising, | ||
Dict(1=>4, 2=>2), | ||
energy=energy, | ||
spectrum = brute_force | ||
) | ||
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for origin ∈ (:NW, :SW) | ||
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β = 2. | ||
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x, y = m, n | ||
peps = PepsNetwork(x, y, fg, β, origin) | ||
pp = PEPSRow(peps, 1) | ||
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# the solution without cutting off | ||
M1 = pp[1][1,1,:,1,:] | ||
M2 = pp[2][:,1,1,1,:] | ||
@reduce MM[a,b] |= sum(x) M1[x,a] * M2[x,b] | ||
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_, inds = findmax(MM) | ||
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A1ex, A2ex, C = make_particular_tensors(D) | ||
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@test pp[1] ≈ A1ex.^β | ||
@test pp[2] ≈ A2ex.^β | ||
@test MM ≈ transpose(C.^β) | ||
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# peps solution, first tensor | ||
Aa1 = pp[1] | ||
Aa2 = MPO(pp)[2] | ||
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@reduce A12[l, u, d, uu, rr, dd, σ] |= sum(x) Aa1[l, u, x, d, σ] * Aa2[x, uu, rr, dd] | ||
A12 = dropdims(A12, dims=(1,2,3,4,5,6)) | ||
_, spins = findmax(A12) | ||
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#solution from the first tensor | ||
st = get_prop(fg, 1, :spectrum).states | ||
@test st[spins] == sol_A1 | ||
@test st[inds[1]] == sol_A1 | ||
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# reading projector | ||
p1, en, p2 = projectors(fg, 1, 2) | ||
if D[(1, 2)] == 0.652 | ||
@test p1 == [1.0 0.0; 0.0 1.0; 1.0 0.0; 0.0 1.0] | ||
@test en == [0.73 -0.73; -0.73 0.73] | ||
@test p2 == [1.0 0.0; 0.0 1.0] | ||
end | ||
r1, rn, r2 = projectors(fg, 2, 1) | ||
@test p1 == r2 | ||
@test p2 == r1 | ||
@test en == rn | ||
@test projectors(fg, 3, 1) == (ones(1,1), ones(1,1), ones(1,1)) | ||
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@reduce C[a, b, c, d] := sum(x) p1[$spins, x] * pp[$2][x, a, b, c, d] | ||
_, s = findmax(C[1,1,1,:]) | ||
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# solution form the second tensor | ||
st = get_prop(fg, 2, :spectrum).states | ||
@test st[s] == sol_A2 | ||
@test st[inds[2]] == sol_A2 | ||
end | ||
end | ||
end | ||
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@testset "larger example" begin | ||
# grid | ||
# A1 | A2 | ||
# | | ||
# 1 -- 3 -|- 5 -- 7 | ||
# | | | | | | ||
# | | | | | | ||
# 2 -- 4 -|- 6 -- 8 | ||
# | | ||
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D = Dict((5, 7) => -0.0186,(5, 6) => 0.0322,(2, 2) => -0.5289544745642463,(4, 4) => -0.699,(4, 6) => 0.494,(3, 3) => -0.4153941108520631,(8, 8) => 0.696,(6, 8) => 0.552,(1, 3) => -0.739,(7, 8) => -0.0602,(2, 4) => -0.0363,(1, 1) => 0.218,(7, 7) => -0.931,(1, 2) => 0.162,(6, 6) => 0.567,(5, 5) => -0.936,(3, 4) => 0.0595,(3, 5) => -0.9339) | ||
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m = 1 | ||
n = 2 | ||
t = 4 | ||
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L = m * n * t | ||
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g_ising = ising_graph(D, L) | ||
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update_cells!( | ||
g_ising, | ||
rule = square_lattice((m, 1, n, 1, t)), | ||
) | ||
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fg1 = factor_graph( | ||
g_ising, | ||
Dict(1=>16, 2=>16), | ||
energy=energy, | ||
spectrum = brute_force, | ||
) | ||
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fg2 = factor_graph( | ||
g_ising, | ||
Dict(1=>16, 2=>16), | ||
energy=energy, | ||
spectrum = full_spectrum, | ||
) | ||
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for fg in [fg1, fg2] | ||
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#Partition function | ||
β = 2. | ||
states = collect.(all_states(rank_vec(g_ising))) | ||
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ρ = exp.(-β .* energy.(states, Ref(g_ising))) | ||
Z = sum(ρ) | ||
@test gibbs_tensor(g_ising, β) ≈ ρ ./ Z | ||
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for origin ∈ (:NW, :SW, :WS, :WN, :NE, :EN, :SE, :ES) | ||
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peps = PepsNetwork(m, n, fg, β, origin) | ||
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ψ = MPO(PEPSRow(peps, 1)) | ||
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for i ∈ 2:peps.i_max | ||
W = MPO(PEPSRow(peps, i)) | ||
M = MPO(peps, i-1, i) | ||
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ψ = (ψ * M) * W | ||
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@test length(W) == peps.j_max | ||
for A ∈ ψ @test size(A, 2) == 1 end | ||
@test size(ψ[1], 1) == 1 == size(ψ[peps.j_max], 3) | ||
end | ||
for A ∈ ψ @test size(A, 4) == 1 end | ||
#println("ψ ", ψ) | ||
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ZZ = [] | ||
for A ∈ ψ | ||
#println("A ", A) | ||
push!(ZZ, dropdims(A, dims=(2, 4))) | ||
#println("ZZ ", ZZ) | ||
end | ||
@test Z ≈ prod(ZZ)[] | ||
end | ||
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origin = :NW | ||
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x, y = m, n | ||
peps = PepsNetwork(x, y, fg, β, origin) | ||
pp = PEPSRow(peps, 1) | ||
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# brute force solution | ||
bf = brute_force(g_ising; num_states = 1) | ||
states = bf.states[1] | ||
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cluster = props(fg, 1)[:cluster] | ||
println(cluster.vertices) | ||
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cluster = props(fg, 2)[:cluster] | ||
println(cluster.vertices) | ||
sol_A1 = states[[1,2,3,4]] | ||
sol_A2 = states[[5,6,7,8]] | ||
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Aa1 = pp[1] | ||
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# A2 traced | ||
# index 1 (left is not trivial) | ||
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Aa2 = MPO(pp)[2] | ||
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# contraction of A1 with A2 | ||
# | ||
# . . | ||
# . . | ||
# A1 -- A2 = A12 | ||
# | ||
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@reduce A12[l, u, d, uu, rr, dd, σ] |= sum(x) Aa1[l, u, x, d, σ] * Aa2[x, uu, rr, dd] | ||
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A12 = dropdims(A12, dims=(1,2,3,4,5,6)) | ||
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_, spins = findmax(A12) | ||
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st = get_prop(fg, 1, :spectrum).states | ||
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@test st[spins] == sol_A1 | ||
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p1, _, _ = projectors(fg, 1, 2) | ||
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@reduce C[a, b, c, d] := sum(x) p1[$spins, x] * pp[$2][x, a, b, c, d] | ||
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_, s = findmax(C[1,1,1,:]) | ||
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st = get_prop(fg, 2, :spectrum).states | ||
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@test st[s] == sol_A2 | ||
end | ||
end |
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