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Fix translation operator in Ising CFT example #304

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Merged
lkdvos merged 10 commits into from
Jul 4, 2025
Merged

Fix translation operator in Ising CFT example #304

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1a211c4
Update Ising CFT example
leburgel Jul 3, 2025
dbfb386
Update example checksum to use relative path
leburgel Jul 3, 2025
5909179
Regenerate examples with updated hashes
leburgel Jul 3, 2025
8153813
Proper semicolons for clarity
leburgel Jul 3, 2025
df15d94
Don't blind copy things
leburgel Jul 3, 2025
bb698c5
Reregenerate examples
leburgel Jul 4, 2025
e47d746
Once more but with labels
leburgel Jul 4, 2025
8013e8f
Actually use the MPS results
leburgel Jul 4, 2025
4f11b58
Try that again
leburgel Jul 4, 2025
1199eb9
Actually use MPS data, plot against conformal spin to remove size dep…
leburgel Jul 4, 2025
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86 changes: 43 additions & 43 deletions docs/src/examples/classic2d/1.hard-hexagon/index.md
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6 changes: 3 additions & 3 deletions docs/src/examples/classic2d/1.hard-hexagon/main.ipynb
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Expand Up @@ -145,11 +145,11 @@
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.4"
"version": "1.10.4"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.4",
"name": "julia-1.10",
"display_name": "Julia 1.10.4",
"language": "julia"
}
},
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541 changes: 271 additions & 270 deletions docs/src/examples/quantum1d/1.ising-cft/index.md
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63 changes: 37 additions & 26 deletions docs/src/examples/quantum1d/1.ising-cft/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -96,8 +96,8 @@
"cell_type": "code",
"source": [
"function O_shift(L)\n",
" τ = BraidingTensor{ComplexF64}(ℂ^2, ℂ^2)\n",
" O = TensorMap(τ)\n",
" I = id(ComplexF64, ℂ^2)\n",
" @tensor O[W S; N E] := I[W; N] * I[S; E]\n",
" return periodic_boundary_conditions(InfiniteMPO([O]), L)\n",
"end"
],
Expand All @@ -112,7 +112,8 @@
"eigenvalues. The eigensolver will find an orthonormal basis within each energy subspace, but\n",
"this basis is not necessarily a basis of eigenstates of the translation operator. In order\n",
"to fix this, we diagonalize the translation operator within each energy subspace.\n",
"The resulting energy levels have one-to-one correspondence to the operators in CFT, where the momentum is related to their conformal spin as $P_n = \\frac{2\\pi}{L}S_n$."
"The resulting energy levels have one-to-one correspondence to the operators in CFT, where\n",
"the momentum is related to their conformal spin as $P_n = \\frac{2\\pi}{L}S_n$."
],
"metadata": {}
},
Expand Down Expand Up @@ -149,7 +150,10 @@
{
"cell_type": "markdown",
"source": [
"Calculating scaling dimensions from the energy gap"
"We can compute the scaling dimensions $\\Delta_n$ of the operators in the CFT from the\n",
"energy gap of the corresponding excitations as $E_n - E_0 = \\frac{2\\pi v}{L} \\Delta_n$,\n",
"where $v = 2$. If we plot these scaling dimensions against the conformal spin $S_n$ from\n",
"above, we retrieve the familiar spectrum of the Ising CFT."
],
"metadata": {}
},
Expand All @@ -159,9 +163,12 @@
"source": [
"v = 2.0\n",
"Δ = real.(energies[1:18] .- energies[1]) ./ (2π * v / L)\n",
"p = plot(momenta, real.(Δ);\n",
" seriestype=:scatter, xlabel=\"momentum\", ylabel=\"energy\", legend=false)\n",
"vline!(p, [2π / L * i for i in -3:3]; color=\"gray\", linestyle=:dash)\n",
"S = momenta ./ (2π / L)\n",
"\n",
"p = plot(S, real.(Δ);\n",
" seriestype=:scatter, xlabel=\"conformal spin (S)\", ylabel=\"scaling dimension (Δ)\",\n",
" legend=false)\n",
"vline!(p, -3:3; color=\"gray\", linestyle=:dash)\n",
"hline!(p, [0, 1 / 8, 1, 9 / 8, 2, 17 / 8]; color=\"gray\", linestyle=:dash)\n",
"p"
],
Expand Down Expand Up @@ -203,27 +210,31 @@
"outputs": [],
"cell_type": "code",
"source": [
"E_ex, qps = excitations(H_mps, QuasiparticleAnsatz(), ψ, envs; num=16)\n",
"E_ex, qps = excitations(H_mps, QuasiparticleAnsatz(), ψ, envs; num=18)\n",
"states_mps = vcat(ψ, map(qp -> convert(FiniteMPS, qp), qps))\n",
"E_mps = map(x -> expectation_value(x, H_mps), states_mps)\n",
"energies_mps = map(x -> expectation_value(x, H_mps), states_mps)\n",
"\n",
"momenta_mps = Float64[]\n",
"append!(momenta_mps, fix_degeneracies(states[1:1]))\n",
"append!(momenta_mps, fix_degeneracies(states[2:2]))\n",
"append!(momenta_mps, fix_degeneracies(states[3:3]))\n",
"append!(momenta_mps, fix_degeneracies(states[4:5]))\n",
"append!(momenta_mps, fix_degeneracies(states[6:9]))\n",
"append!(momenta_mps, fix_degeneracies(states[10:11]))\n",
"append!(momenta_mps, fix_degeneracies(states[12:12]))\n",
"append!(momenta_mps, fix_degeneracies(states[13:16]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[1:1]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[2:2]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[3:3]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[4:5]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[6:9]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[10:11]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[12:12]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[13:16]))\n",
"append!(momenta_mps, fix_degeneracies(states_mps[17:18]))\n",
"\n",
"v = 2.0\n",
"Δ = real.(energies[1:18] .- energies[1]) ./ (2π * v / L)\n",
"plot(momenta_mps, Δ;\n",
" seriestype=:scatter, xlabel=\"momentum\", ylabel=\"energy\", legend=false)\n",
"vline!(p, [2π / L * i for i in -3:3]; color=\"gray\", linestyle=:dash)\n",
"hline!(p, [0, 1 / 8, 1, 9 / 8, 2, 17 / 8]; color=\"gray\", linestyle=:dash)\n",
"p"
"Δ_mps = real.(energies_mps[1:18] .- energies_mps[1]) ./ (2π * v / L_mps)\n",
"S_mps = momenta_mps ./ (2π / L_mps)\n",
"\n",
"p_mps = plot(S_mps, real.(Δ_mps);\n",
" seriestype=:scatter, xlabel=\"conformal spin (S)\",\n",
" ylabel=\"scaling dimension (Δ)\", legend=false)\n",
"vline!(p_mps, -3:3; color=\"gray\", linestyle=:dash)\n",
"hline!(p_mps, [0, 1 / 8, 1, 9 / 8, 2, 17 / 8]; color=\"gray\", linestyle=:dash)\n",
"p_mps"
],
"metadata": {},
"execution_count": null
Expand All @@ -244,11 +255,11 @@
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.5"
"version": "1.10.4"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.5",
"name": "julia-1.10",
"display_name": "Julia 1.10.4",
"language": "julia"
}
},
Expand Down
222 changes: 112 additions & 110 deletions docs/src/examples/quantum1d/2.haldane/index.md
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6 changes: 3 additions & 3 deletions docs/src/examples/quantum1d/2.haldane/main.ipynb
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Expand Up @@ -187,11 +187,11 @@
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.4"
"version": "1.10.4"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.4",
"name": "julia-1.10",
"display_name": "Julia 1.10.4",
"language": "julia"
}
},
Expand Down
32 changes: 16 additions & 16 deletions docs/src/examples/quantum1d/3.ising-dqpt/index.md
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Expand Up @@ -39,13 +39,14 @@ H₀ = transverse_field_ising(FiniteChain(L); g=-0.5)
````

````
[ Info: DMRG init: obj = +9.627138678740e+00 err = 1.5287e-01
[ Info: DMRG 1: obj = -2.040021714898e+01 err = 1.5582585194e-02 time = 0.10 sec
[ Info: DMRG 2: obj = -2.040021715175e+01 err = 3.4655395009e-07 time = 0.02 sec
[ Info: DMRG 3: obj = -2.040021763026e+01 err = 3.7385206468e-05 time = 0.06 sec
[ Info: DMRG 4: obj = -2.040021786702e+01 err = 2.1782648849e-06 time = 0.04 sec
[ Info: DMRG 5: obj = -2.040021786703e+01 err = 1.3998187485e-07 time = 0.02 sec
[ Info: DMRG conv 6: obj = -2.040021786703e+01 err = 9.0384912069e-11 time = 0.26 sec
[ Info: DMRG init: obj = +9.906929661608e+00 err = 1.4654e-01
[ Info: DMRG 1: obj = -2.040021714938e+01 err = 9.3181641986e-04 time = 0.05 sec
[ Info: DMRG 2: obj = -2.040021715179e+01 err = 2.4688856530e-07 time = 0.03 sec
[ Info: DMRG 3: obj = -2.040021786221e+01 err = 4.2747944525e-05 time = 0.08 sec
[ Info: DMRG 4: obj = -2.040021786699e+01 err = 1.6446674043e-06 time = 0.04 sec
[ Info: DMRG 5: obj = -2.040021786703e+01 err = 2.4678293656e-07 time = 0.03 sec
[ Info: DMRG 6: obj = -2.040021786703e+01 err = 2.3749087526e-10 time = 0.03 sec
[ Info: DMRG conv 7: obj = -2.040021786703e+01 err = 4.3310784899e-12 time = 0.29 sec

````

Expand Down Expand Up @@ -111,14 +112,13 @@ H₀ = transverse_field_ising(; g=-0.5)
````

````
[ Info: VUMPS init: obj = +4.981979532800e-01 err = 3.9530e-01
[ Info: VUMPS 1: obj = -1.030701827098e+00 err = 1.0340065851e-01 time = 6.72 sec
[ Info: VUMPS 2: obj = -1.063544326030e+00 err = 2.9155624606e-04 time = 0.01 sec
[ Info: VUMPS 3: obj = -1.063544409971e+00 err = 1.8767724186e-06 time = 0.01 sec
[ Info: VUMPS 4: obj = -1.063544409973e+00 err = 2.0959736412e-08 time = 0.00 sec
[ Info: VUMPS 5: obj = -1.063544409973e+00 err = 2.7005924256e-09 time = 0.00 sec
[ Info: VUMPS 6: obj = -1.063544409973e+00 err = 3.0434524435e-10 time = 0.00 sec
[ Info: VUMPS conv 7: obj = -1.063544409973e+00 err = 2.4566755222e-11 time = 6.75 sec
[ Info: VUMPS init: obj = +4.937592959715e-01 err = 3.8640e-01
[ Info: VUMPS 1: obj = -1.041532472680e+00 err = 1.0207037612e-01 time = 7.91 sec
[ Info: VUMPS 2: obj = -1.063544395012e+00 err = 1.0570052184e-04 time = 0.01 sec
[ Info: VUMPS 3: obj = -1.063544409972e+00 err = 1.3451291600e-06 time = 0.01 sec
[ Info: VUMPS 4: obj = -1.063544409973e+00 err = 2.1982905922e-08 time = 0.00 sec
[ Info: VUMPS 5: obj = -1.063544409973e+00 err = 8.6218866571e-10 time = 0.00 sec
[ Info: VUMPS conv 6: obj = -1.063544409973e+00 err = 7.1345139950e-11 time = 7.94 sec

````

Expand All @@ -130,7 +130,7 @@ dot(ψ₀, ψ₀)
````

````
1.0000000000000053 - 8.519001927175606e-17im
0.9999999999999991 + 5.43344267830843e-16im
````

so the loschmidth echo takes on the pleasant form
Expand Down
6 changes: 3 additions & 3 deletions docs/src/examples/quantum1d/3.ising-dqpt/main.ipynb
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Expand Up @@ -285,11 +285,11 @@
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.4"
"version": "1.10.4"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.4",
"name": "julia-1.10",
"display_name": "Julia 1.10.4",
"language": "julia"
}
},
Expand Down
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