TN_tutorial3.ipynb

{
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   "source": [
    "### Many-body Entanglement and Tensor Networks\n",
    "Tutorials based on the 2017 Perimeter Scholar International Condensed Matter Review course taught by Guifre Vidal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1a6c9fc",
   "metadata": {},
   "source": [
    "# <span style=\"color:#0C45A9\">Python tutorial 3</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83fe4c7e",
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   "source": [
    "In this tutorial we will obtain universal conformal field theory data from our quantum Ising spin chain model. We will observe finite size effects which originate from the numerical simulation, and would fade as $N\\to\\infty$. In this notebook we won't fully diagonalise our matrices, but we will use **sparce diagonalisation** through the _scipy.sparse.linalg.eigs()_ function. We will carry out the following calculations for PBC and APBC. <br>\n",
    "We will do this by **simultaneously diagonalising** $H,T,S$: the Hamiltonian ($H$), the translation operator ($T$) and the spin flip operator ($S$), since they are symmetries of the sytem:<br>\n",
    "<br>\n",
    "<center> $H \\left\\vert \\psi_{\\alpha} \\right \\rangle = E_{\\alpha}\\left\\vert \\psi_{\\alpha} \\right \\rangle  $ <center> \n",
    "    <br>\n",
    "<center> $T \\left\\vert \\psi_{\\alpha} \\right \\rangle = e^{iK_{\\alpha}}\\left\\vert \\psi_{\\alpha} \\right \\rangle  $ <center>\n",
    "    <br>\n",
    "<center> $S \\left\\vert \\psi_{\\alpha} \\right \\rangle = (-1)^{p_{\\alpha}}\\left\\vert \\psi_{\\alpha} \\right \\rangle  $ <center> <br>\n",
    "    \n",
    "From the diagonalisation , we can get $E_{\\alpha}$, $K_{\\alpha}$ and $p_{\\alpha}$ from: <br>\n",
    "<center> $ E_{\\alpha} = \\left \\langle  \\psi_{\\alpha} \\right \\vert H \\left\\vert \\psi_{\\alpha} \\right \\rangle $<center>\n",
    "<br>\n",
    "<center> $ e^{iK_{\\alpha}} = \\left \\langle  \\psi_{\\alpha} \\right \\vert T \\left\\vert \\psi_{\\alpha} \\right \\rangle \\; \\to \\; K_{\\alpha}= \\text{angle}\\left( \\left \\langle  \\psi_{\\alpha} \\right \\vert T \\left\\vert \\psi_{\\alpha} \\right \\rangle\\right) $ <center>\n",
    "<br>\n",
    "<center> $ p_{\\alpha} = \\frac{1-\\left \\langle  \\psi_{\\alpha} \\right \\vert \\, S\\, \\left\\vert \\psi_{\\alpha} \\right \\rangle }{2} $ <center>\n",
    " <br>\n",
    "    \n",
    "Finally, we can get the CFT **scaling dimension** ($\\Delta_{\\alpha}$) and **conformal spin** ($S_{\\alpha}$): <br>\n",
    "<br>\n",
    "<center> $ E_{\\alpha} = A + \\frac{B}{N}\\left(\\Delta_{\\alpha}-\\frac{c}{12} \\right) + \\mathcal{O}\\left(\\frac{1}{N^2}\\right)  \\quad\\quad \\to  \\quad\\quad E_{\\alpha} - E_0 = \\frac{B}{N}(\\Delta_{\\alpha}-\\Delta_0)$<center>   \n",
    "    <br>\n",
    "    <center> $ K_{\\alpha} = \\frac{2\\pi}{N}S_{\\alpha} \\quad\\quad \\to \\quad\\quad \\boxed{S_{\\alpha} = \\frac{N}{2\\pi}K_{\\alpha}}$  <center>    \n",
    " <br>\n",
    " \n",
    " However, we still don't know $B$ but we can use the relation:\n",
    " <center> $\\frac{E_{\\alpha}-E_0}{E_1-E_0}=\\frac{\\Delta_{\\alpha}-\\Delta_0}{\\Delta_1-\\Delta_0} \\quad \\to \\quad \\boxed{\\Delta_{\\alpha} = (\\Delta_1-\\Delta_0)\\frac{E_{\\alpha}-E_0}{E_1-E_0}+\\Delta_0}$. <br>\n",
    " <br>\n",
    "     \n",
    " For **PBC** we have $\\Delta_0 = 0$ and $\\Delta_1=1/8$, so: $\\boxed{\\Delta_{\\alpha}^{PBC} = \\frac{1}{8}\\frac{E_{\\alpha}-E_0}{E_1-E_0}}$<br>\n",
    " For **APBC** we have $\\Delta_0 = 1/8$ and $\\Delta_1=1/2$, so: $\\boxed{\\Delta_{\\alpha}^{APBC} = \\frac{3}{8}\\frac{E_{\\alpha}-E_0}{E_1-E_0}+\\frac{1}{8}}$<br>"
   ]
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   "cell_type": "markdown",
   "id": "03f2bc70",
   "metadata": {},
   "source": [
    "## 3.1. Conformal field theory (CFT) data for PBC quantum Ising model on $N$ spins"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15d0ab81",
   "metadata": {},
   "source": [
    "Define the Hamiltonian for the quantum Ising model as per the previous tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "903a9b8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def qIsingH(N, h, bc = 1): #bc = 1 PBC, =-1 APBC\n",
    "    I = np.eye(2) #2x2 identity matrix\n",
    "    X = np.array([[0,1],[1,0]]) #Pauli-X\n",
    "    Z = np.array([[1,0],[0,-1]]) #Pauli-Z\n",
    "    XX = np.kron(X,X) \n",
    "    H = -XX - h*(np.kron(Z,I) + np.kron(I,Z)) #Hamiltonian for N=2\n",
    "    \n",
    "    for n in range(3,(N+1)):\n",
    "        H = np.kron(H,I)-np.kron(np.eye(2**(n-2)),XX)-h*np.kron(np.eye(2**(n-1)),Z)\n",
    "\n",
    "    H = H - bc*np.kron(X,np.kron(np.eye(2**(N-2)),X))\n",
    "    \n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98a70a3e",
   "metadata": {},
   "source": [
    "### 3.1.1. Translation and parity operators: symmetries"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d9dc56e",
   "metadata": {},
   "source": [
    "#### Translation operator, $T$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10695d2a",
   "metadata": {},
   "source": [
    "Define the translator operator $T$ which acts by mapping spin $m \\to m+1$ such that $T\\left\\vert s_1 s_2 s_3 \\right \\rangle = \\left\\vert s_3 s_1 s_2 \\right \\rangle$ and $T\\,\\sigma_m^{\\alpha}\\, T^{\\dagger}= \\sigma_{m=1}^{\\alpha}$. Our Hamiltonian is invariant under translations: $[H,T] = 0$. We also know that momentum is the generator of translations: $T \\to P_{\\alpha}$ <br>\n",
    "We will build this operator from the _SWAP_ operator on $N=2$. The _SWAP_ operator acts on two spins the following way: $SWAP\\left\\vert s_1 s_2 \\right \\rangle = \\left\\vert s_2 s_1 \\right \\rangle$.<br>\n",
    "If $T$ needs to be built for APBC, we multiply the $T$ operator for PBC by an diagonal matrix with $\\{-1,1\\}$ that accounts for the APBC position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "28236d75",
   "metadata": {},
   "outputs": [],
   "source": [
    "def T_op(N, APBC = False):\n",
    "    SWAP = np.array([[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]) #SWAP operator\n",
    "    I = np.eye(2)\n",
    "    T = SWAP\n",
    "    SWAP_N = SWAP #SWAP for N spins that we will build\n",
    "    \n",
    "    for n in range(3,(N+1)):\n",
    "        T = np.kron(T,I)\n",
    "        SWAP_N = np.kron(I, SWAP_N)\n",
    "        T = T.dot(SWAP_N)\n",
    "    \n",
    "    if APBC:\n",
    "        Z = np.array([[1,0],[0,-1]]) #Pauli-Z\n",
    "        ZI = np.kron(Z, np.eye(2**(N-1)))\n",
    "        T = ZI.dot(T)\n",
    "        \n",
    "    return T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58334bd9",
   "metadata": {},
   "source": [
    "#### Spin flip operator, $S$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01ce48f7",
   "metadata": {},
   "source": [
    "This operator applies the Pauli-$Z$ operator to all the qubits: $S = \\sigma_1^z \\otimes \\sigma_2^z \\otimes \\cdots \\otimes \\sigma_N^z$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "170d3bdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def S_op(N):\n",
    "    Z = np.array([[1,0],[0,-1]]) #Pauli-Z\n",
    "    Z_2 = Z\n",
    "\n",
    "    for n in range(2,(N+1)):\n",
    "        Z_2 = np.kron(Z_2,Z)\n",
    "        \n",
    "    S = Z_2\n",
    "    return S"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "411c73b3",
   "metadata": {},
   "source": [
    "### 3.1.2. Define Hamiltonian"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd515ad2",
   "metadata": {},
   "source": [
    "We want to simulatenously diagonalise $H,T$ and $S$, so we consider $H = H+\\alpha HT + \\beta HS$. We choose $\\alpha$ and $\\beta$ such that the scales of the entries of $H$, $HT$ and $HS$ are very different. \n",
    "<br>Note that $T$ is non-hermitian, so some eigenvalues will be complex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "83133b55",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10 #Hamiltonian will be 2^N x 2^N\n",
    "h = 1\n",
    "\n",
    "H_TFIM = qIsingH(N,h) #PBC quantum Ising\n",
    "H_TFIM -= 4*N*np.eye(2**N) #make all eigenvalues negative\n",
    "T = T_op(N)\n",
    "S = S_op(N)\n",
    "\n",
    "H_final = H_TFIM.dot(np.eye(2**N) + 0.001*T +0.00001*S)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efa820c0",
   "metadata": {},
   "source": [
    "### 3.1.3. Sparse diagonalisation method: largest eigenvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "573e1beb",
   "metadata": {},
   "source": [
    "We obtain only the _num_states_ eigenvectors with smallest energy eigenvalues. This is done by using a Fortran package called _ARPACK_, which provides routines for quickly finding a few eigenvalues/eigenvectors of large sparse matrices. All of the functionality provided in _ARPACK_ is contained within the high-level interface _scipy.sparse.linalg.eigs_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3ad9fe6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse.linalg import eigs\n",
    "\n",
    "num_states = 12\n",
    "\n",
    "D, Psi = eigs(H_final, k = num_states, which = 'LM')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac2f2049",
   "metadata": {},
   "source": [
    "### 3.1.4. Obtain $E_{\\alpha}$, $K_{\\alpha}$, $p_{\\alpha}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d128c77",
   "metadata": {},
   "source": [
    "Evaluate the energy $E$, momentum $K$ and parity $p$ on the obtained eigenvectors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d915c8f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "E = np.real(np.diag((Psi.conj().T).dot(H_TFIM).dot(Psi))) + 4*N #shift back\n",
    "k = np.angle(np.diag((Psi.conj().T).dot(T).dot(Psi)))\n",
    "p = np.diag((Psi.conj().T).dot(S).dot(Psi))\n",
    "p = abs(np.real(((1-p)/2).round()))\n",
    "\n",
    "#sort from smaller to largest\n",
    "ord_idx = np.argsort(E)\n",
    "E = E[ord_idx]\n",
    "k = k[ord_idx] \n",
    "p = p[ord_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0bc3078a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy: [-12.78490644 -12.62750303 -11.53343072 -11.39143505 -11.39143505\n",
      " -10.34320658 -10.34320658 -10.34320658 -10.34320658 -10.27636202\n",
      " -10.27636202 -10.15536707] \n",
      "Momentum: [ 0.          0.          0.         -0.62831853  0.62831853 -1.25663706\n",
      "  1.25663706 -0.62831853  0.62831853 -1.25663706  1.25663706  0.        ] \n",
      "Parity: [0. 1. 0. 1. 1. 0. 0. 0. 0. 1. 1. 1.]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Energy: %s \\nMomentum: %s \\nParity: %s\\n' %(E,k,p))\n",
    "E_unique = np.unique(E)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8681ed15",
   "metadata": {},
   "source": [
    "### 3.1.5. Numerical estimates of $\\Delta_{\\alpha}$ and $S_{\\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8fd5e2de",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaling_dim = (1/8)*(E-E[0])/(E[1]-E[0])\n",
    "conf_spin = k/(2*np.pi)*N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fac61c53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaling dimension: [0.         0.125      0.99384417 1.1066083  1.1066083  1.93904614\n",
      " 1.93904614 1.93904614 1.93904614 1.99212994 1.99212994 2.0882166 ] \n",
      "Conformal spin: [ 0.  0.  0. -1.  1. -2.  2. -1.  1. -2.  2.  0.]\n"
     ]
    }
   ],
   "source": [
    "print('Scaling dimension: %s \\nConformal spin: %s' %(scaling_dim, conf_spin))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c9d2776",
   "metadata": {},
   "source": [
    "### 3.1.6. Plot theory vs numerical CFT data comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "30f7d331",
   "metadata": {},
   "outputs": [],
   "source": [
    "th_scaling_dim = [0, 1/8, 1, 1+1/8, 1+1/8, 2, 2, 2, 2, 2+1/8, 2+1/8, 2+1/8]\n",
    "th_parity = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]\n",
    "th_conf_spin = [0,  0,  0,  -1, 1,  -1, 1,  -2,  2,  -2,  2,  0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1d4feff3",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "<matplotlib.legend.Legend at 0x21b7633ca90>"
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     "execution_count": 11,
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\n",
      "text/plain": [
       "<Figure size 1296x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, layout=\"constrained\", figsize=(18, 9))\n",
    "fig.suptitle('PBC Ising CFT numerical vs theoretical data\\n', fontsize=30)\n",
    "ax1.set_xlabel(r\"conformal spin, $S_{\\alpha}$\", fontsize=20)\n",
    "ax2.set_xlabel(r\"conformal spin, $S_{\\alpha}$\", fontsize=20)\n",
    "ax1.set_ylabel(r\"scaling dimension, $\\Delta_{\\alpha}$\", fontsize=20)\n",
    "ax2.set_ylabel(r\"scaling dimension, $\\Delta_{\\alpha}$\", fontsize=20)\n",
    "ax1.set_title(r'Even parity, $p=0$', fontsize=25)\n",
    "ax2.set_title(r'Odd parity, $p=1$', fontsize=25)\n",
    "ax1.tick_params(axis='both', labelsize=18)\n",
    "ax2.tick_params(axis='both', labelsize=18)\n",
    "ax1.grid()\n",
    "ax2.grid()\n",
    "ax1.set_xlim([-3, 3])\n",
    "ax2.set_xlim([-3, 3])\n",
    "ax1.set_ylim([-0.2, 2.8])\n",
    "ax2.set_ylim([-0.2, 2.8])\n",
    "ax1.text(0.07,1.07,r\"$\\epsilon$ energy density\", fontsize=20, color='grey')\n",
    "ax1.text(0.07,0.07,r\"$\\mathbb{1}$ identity\", fontsize=20, color='grey')\n",
    "ax2.text(0.07,1/8+0.07,r\"$\\sigma$ spin\", fontsize=20, color='grey')\n",
    "\n",
    "for i in range(len(th_parity)):\n",
    "    if th_parity[i] == 0:\n",
    "        ax1.plot(th_conf_spin[i], th_scaling_dim[i], marker = \"s\", color = \"y\", markeredgecolor= \"black\", ms=15)\n",
    "    elif th_parity[i] == 1:\n",
    "        ax2.plot(th_conf_spin[i], th_scaling_dim[i], marker = \"s\", color = \"y\", markeredgecolor= \"black\", ms=15)\n",
    "\n",
    "\n",
    "for i in range(num_states):\n",
    "    if p[i] == 0:\n",
    "        ax1.plot(conf_spin[i], scaling_dim[i], marker = \"o\", color = \"b\", ms=10)\n",
    "    elif p[i] == 1:\n",
    "        ax2.plot(conf_spin[i], scaling_dim[i], marker = \"o\", color = \"b\", ms=10)\n",
    "\n",
    "from matplotlib.lines import Line2D\n",
    "from matplotlib.patches import Patch\n",
    "legend_elements = [Line2D([0], [0], marker='o', color='w', label='Numerical',\n",
    "                          markerfacecolor='b', markersize=15),\n",
    "                   Patch(facecolor='y', edgecolor='black',\n",
    "                         label='Theory')]\n",
    "\n",
    "        \n",
    "ax1.legend(handles=legend_elements, fontsize=15)\n",
    "ax2.legend(handles=legend_elements, fontsize=15)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db89e826",
   "metadata": {},
   "source": [
    "## 3.2. Conformal field theory (CFT) data for APBC quantum Ising model on $N$ spins"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "842a9e6b",
   "metadata": {},
   "source": [
    "### 3.2.1. Define Hamiltonians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dd586c89",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10 #Hamiltonian will be 2^N x 2^N\n",
    "h = 1\n",
    "\n",
    "H_TFIM = qIsingH(N,h, bc = -1) #APBC quantum Ising\n",
    "H_TFIM -= 4*N*np.eye(2**N) #make all eigenvalues negative\n",
    "T = T_op(N, APBC = True)\n",
    "S = S_op(N)\n",
    "\n",
    "H_final = H_TFIM.dot(np.eye(2**N) + 0.001*T +0.00001*S)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d73980d",
   "metadata": {},
   "source": [
    "### 3.2.2. Sparse diagonalisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ead31d18",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse.linalg import eigs\n",
    "\n",
    "num_states = 14\n",
    "\n",
    "D, Psi = eigs(H_final, k = num_states, which = 'LM')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "602c6b26",
   "metadata": {},
   "source": [
    "### 3.2.3. Obtain $E_{\\alpha}$, $k_{\\alpha}$, $p_{\\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "06081798",
   "metadata": {},
   "outputs": [],
   "source": [
    "E = np.real(np.diag((Psi.conj().T).dot(H_TFIM).dot(Psi))) + 4*N #shift back\n",
    "k = np.angle(np.diag((Psi.conj().T).dot(T).dot(Psi)))\n",
    "p = np.diag((Psi.conj().T).dot(S).dot(Psi))\n",
    "p = abs(np.real(((1-p)/2).round()))\n",
    "\n",
    "#sort from smaller to largest\n",
    "ord_idx = np.argsort(E)\n",
    "E = E[ord_idx]\n",
    "k = k[ord_idx] \n",
    "p = p[ord_idx]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4165c32",
   "metadata": {},
   "source": [
    "### 3.2.4. Numerical estimates of $\\Delta_{\\alpha}$ and $S_{\\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "31181eef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaling dimension: [0.125      0.5        0.5        1.11473179 1.11473179 1.45302418\n",
      " 1.45302418 2.00758174 2.00758174 2.10446359 2.26371497 2.26371497\n",
      " 2.4550931  2.4550931 ] \n",
      "Conformal spin: [ 0.  -0.5  0.5 -1.   1.  -1.5  1.5 -2.   2.   0.  -2.5  2.5 -1.5  1.5]\n"
     ]
    }
   ],
   "source": [
    "scaling_dim = (3/8)*(E-E[0])/(E[1]-E[0]) + 1/8\n",
    "conf_spin = k/(2*np.pi)*N\n",
    "\n",
    "print('Scaling dimension: %s \\nConformal spin: %s' %(scaling_dim, conf_spin))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e738901",
   "metadata": {},
   "source": [
    "### 3.2.5. Plot theory vs numerical CFT data comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "accac3c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "th_scaling_dim = [1/8, 1/2, 1/2, 1+1/8, 1+1/8, 1+1/2, 1+1/2, 2+1/8, 2+1/8, 2+1/8, 2+1/2, 2+1/2, 2+1/2, 2+1/2]\n",
    "th_parity = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]\n",
    "th_conf_spin = [0, -0.5, 0.5, -1, 1, -1.5, 1.5, -2, 2, 0, -2.5, 2.5, -1.5,  1.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6bb6fc92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x21b76301190>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, layout=\"constrained\", figsize=(18, 9))\n",
    "fig.suptitle('APBC Ising CFT numerical vs theoretical data\\n', fontsize=30)\n",
    "ax1.set_xlabel(r\"conformal spin, $S_{\\alpha}$\", fontsize=20)\n",
    "ax2.set_xlabel(r\"conformal spin, $S_{\\alpha}$\", fontsize=20)\n",
    "ax1.set_ylabel(r\"scaling dimension, $\\Delta_{\\alpha}$\", fontsize=20)\n",
    "ax2.set_ylabel(r\"scaling dimension, $\\Delta_{\\alpha}$\", fontsize=20)\n",
    "ax1.set_title(r'Even parity, $p=0$', fontsize=25)\n",
    "ax2.set_title(r'Odd parity, $p=1$', fontsize=25)\n",
    "ax1.tick_params(axis='both', labelsize=18)\n",
    "ax2.tick_params(axis='both', labelsize=18)\n",
    "ax1.grid()\n",
    "ax2.grid()\n",
    "ax1.set_xlim([-3, 3])\n",
    "ax2.set_xlim([-3, 3])\n",
    "ax1.set_ylim([-0.2, 2.8])\n",
    "ax2.set_ylim([-0.2, 2.8])\n",
    "ax1.text(0.17,0.09,r\"$\\mu$ disorder\", fontsize=20, color='grey')\n",
    "ax2.text(0.42,0.6,r\"$\\Psi$\", fontsize=20, color='grey')\n",
    "ax2.text(-0.57,0.6,r\"$\\bar{\\Psi}$\", fontsize=20, color='grey')\n",
    "ax2.text(-0.45,0.3,\"fermions\", fontsize=20, color='grey')\n",
    "\n",
    "for i in range(len(th_parity)):\n",
    "    if th_parity[i] == 0:\n",
    "        ax1.plot(th_conf_spin[i], th_scaling_dim[i], marker = \"s\", color = \"y\", markeredgecolor= \"black\", ms=15)\n",
    "    elif th_parity[i] == 1:\n",
    "        ax2.plot(th_conf_spin[i], th_scaling_dim[i], marker = \"s\", color = \"y\", markeredgecolor= \"black\", ms=15)\n",
    "\n",
    "\n",
    "for i in range(num_states):\n",
    "    if p[i] == 0:\n",
    "        ax1.plot(conf_spin[i], scaling_dim[i], marker = \"o\", color = \"b\", ms=10)\n",
    "    elif p[i] == 1:\n",
    "        ax2.plot(conf_spin[i], scaling_dim[i], marker = \"o\", color = \"b\", ms=10)\n",
    "\n",
    "from matplotlib.lines import Line2D\n",
    "from matplotlib.patches import Patch\n",
    "legend_elements = [Line2D([0], [0], marker='o', color='w', label='Numerical',\n",
    "                          markerfacecolor='b', markersize=15),\n",
    "                   Patch(facecolor='y', edgecolor='black',\n",
    "                         label='Theory')]\n",
    "\n",
    "        \n",
    "ax1.legend(handles=legend_elements, fontsize=15)\n",
    "ax2.legend(handles=legend_elements, fontsize=15)\n"
   ]
  }
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