Data_collection.ipynb

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    "import numpy as np\n",
    "from Initialization import initialize_Ising\n",
    "from opt_3leg import *\n",
    "from tqdm import tqdm\n",
    "from util import *\n",
    "from entanglement_filtering import filter_C4"
   ]
  },
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   "source": [
    "# Collecting of S(L) from TRG\n",
    "\n",
    "\n",
    "Here, we demonstrate how to numerically compute the fixed-point tensor.\n",
    "\n",
    "In order to guarantee the crossing symmetry, we take one of the SVD tensor and patch the other one as a mirror image of the other.\n",
    "\n",
    "In this way, we can prevent unnecessary $D_4$ symmetry breaking from numerical errors."
   ]
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     "text": [
      "100%|███████████████████████████████████████████| 20/20 [01:15<00:00,  3.79s/it]\n"
     ]
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   "source": [
    "# Collecting data from TRG\n",
    "Tc = 2/np.log(1+np.sqrt(2))\n",
    "\n",
    "chi_cut = 32\n",
    "tA = initialize_Ising(Tc)\n",
    "tA,_,norm =  normalize_tensor(tA,tA.transpose(1,2,3,0))\n",
    "for i in tqdm(range(20)):\n",
    "    tA = filter_C4(tA)\n",
    "    S,_s = SVD12(tA,chi_cut,cutoff = 1e-14)\n",
    "    del _s\n",
    "    S /= S.flatten()[np.argmax(np.abs(S))]\n",
    "    M = S_to_M(S)\n",
    "    np.save(\"S_data/3_leg_S_D_{}_step_{}.npy\".format(chi_cut,i+1),S)\n",
    "    tA = np.einsum(\"ijkl,nkjm->mnli\",M,M)\n",
    "    tA /= np.einsum(\"ijij\",tA)"
   ]
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    "\n",
    "\n",
    "# Fixing the gauge to the CFT basis\n",
    "## Gauge-fixing of $S^*$\n",
    "\n",
    "To change the basis for the indices to the CFT one, we need to find a unitary matrix that diagonalizes the transfer matrix of the corresponding index. Then, we apply these projectors to the original indices.\n",
    "\n",
    "This gauge-fixing can be done \"gauge_fix(S)\" function in \"util.py\".\n",
    "\n",
    "In order to reduce the memory cost, we project only on the first three states, which corresponds to the three primary state $1,\\ \\sigma,\\ \\epsilon$ for the Ising CFT. "
   ]
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     "text": [
      "D: 32, step: 4\n",
      "D: 32, step: 5\n",
      "D: 32, step: 6\n",
      "D: 32, step: 7\n",
      "D: 32, step: 8\n",
      "D: 32, step: 9\n",
      "D: 32, step: 10\n",
      "D: 32, step: 11\n",
      "D: 32, step: 12\n",
      "D: 32, step: 13\n",
      "D: 32, step: 14\n",
      "D: 32, step: 15\n",
      "D: 32, step: 16\n",
      "D: 32, step: 17\n",
      "D: 32, step: 18\n",
      "D: 32, step: 19\n",
      "D: 32, step: 20\n"
     ]
    }
   ],
   "source": [
    "D_list = [32]\n",
    "step_list = np.arange(4,21,1)\n",
    "for D in D_list:\n",
    "    for step in step_list:\n",
    "        print(\"D: {}, step: {}\".format(D,step))\n",
    "        S = np.load(\"S_data/3_leg_S_D_{}_step_{}.npy\".format(D,step))\n",
    "        np.save(\"Gauge-fixed_S/S_D_{}_step_{}.npy\".format(D,step),gauge_fix(S))"
   ]
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    "\n",
    "## Gauge-fix of $T^*$\n",
    "We do the same procedure to the four-leg fixed-point tensor using \"fp_tensor(S)\" in \"util.py\".\n",
    "The collected data will be analyzed in \"TRG_analysis-Ising.ipynb\".\n",
    "\n",
    "In the directories \"/Gauge-fixed/\" and \"/fptensor/\", we prepared the results from higher bond dimensions up to $D=96$."
   ]
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      "D: 32, step: 4\n"
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      "D: 32, step: 6\n"
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   "source": [
    "D_list = [32]\n",
    "step_list = np.arange(4,21,1)\n",
    "for D in D_list:\n",
    "    for step in step_list:\n",
    "        print(\"D: {}, step: {}\".format(D,step))\n",
    "        S = np.load(\"S_data/3_leg_S_D_{}_step_{}.npy\".format(D,step))\n",
    "        np.save(\"fptensor/Ising_D_{}_step_{}.npy\".format(D,step),fp_tensor(S))"
   ]
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