Fix translation operator in Ising CFT example (#304)

* Update Ising CFT example

* Update example checksum to use relative path

* Regenerate examples with updated hashes

* Proper semicolons for clarity

* Don't blind copy things

* Reregenerate examples

* Once more but with labels

* Actually use the MPS results

* Try that again

* Actually use MPS data, plot against conformal spin to remove size dependency

Author: leburgel

docs/src/examples/classic2d/1.hard-hexagon/index.md

@@ -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"
   }
  },

docs/src/examples/classic2d/1.hard-hexagon/main.ipynb

@@ -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"
    ],
@@ -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": {}
   },
@@ -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": {}
   },
@@ -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"
    ],
@@ -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
@@ -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"
   }
  },

docs/src/examples/quantum1d/1.ising-cft/index.md

@@ -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"
   }
  },

docs/src/examples/quantum1d/1.ising-cft/main.ipynb

@@ -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
 
 ````
 
@@ -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
 
 ````
 
@@ -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

docs/src/examples/quantum1d/2.haldane/index.md

@@ -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"
   }
  },