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      "source": [
        "# Green's Function and TD-DMRG\n",
        "\n",
        "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/block-hczhai/block2-preview/blob/master/docs/source/tutorial/greens-function.ipynb)"
      ],
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        "id": "ctuEMhLVU0O5"
      }
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    {
      "cell_type": "code",
      "source": [
        "!pip install block2==0.5.2rc13 -qq --progress-bar off --extra-index-url=https://block-hczhai.github.io/block2-preview/pypi/\n",
        "!pip install pyscf==2.3.0 -qq --progress-bar off"
      ],
      "metadata": {
        "id": "zlAQvp7RmKRP"
      },
      "execution_count": 1,
      "outputs": []
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      "cell_type": "markdown",
      "source": [
        "In the following example, we calculate the electron removal (IP) part of one-particle Green's function for Hydrogen chain ($\\mathrm{H_6}$) in the minimal basis:\n",
        "\n",
        "$$\n",
        "    G_{ij}^-(\\omega) = \\langle \\Psi_0 | a_j^\\dagger \\frac{1}{\\omega + \\hat{H}_0 - E_0 + i \\eta} a_i |\\Psi_0\\rangle\n",
        "$$\n",
        "\n",
        "where $|\\Psi_0\\rangle$ is the ground state, $i = j = 2$ (counting from zero), $\\eta = 0.005$.\n",
        "\n",
        "The Green's function can be computed using DMRG in either the frequency domain (dynamical DMRG) or the time domain (time-dependent DMRG).\n",
        "\n",
        "## Dynamical DMRG\n",
        "\n",
        "We first solve the response equation to find the Green's function in the frequency domain.\n",
        "\n",
        "Note that the return value of ``driver.greens_function`` method is the state:\n",
        "\n",
        "$$|X_i\\rangle := \\frac{1}{\\omega + \\hat{H}_0 - E_0 + i \\eta} a_i |\\Psi_0\\rangle\n",
        "$$\n",
        "\n",
        "Therefore, to get the value for Green's function with $i\\neq j$, one can simply use ``driver.expectation`` to compute the dot product of $|X_i\\rangle$ with some other $a_j|\\Psi_0\\rangle$.\n",
        "\n",
        "In the ``SU2`` mode:"
      ],
      "metadata": {
        "id": "IqlreH0DVTV2"
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    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from pyblock2._pyscf.ao2mo import integrals as itg\n",
        "from pyblock2.driver.core import DMRGDriver, SymmetryTypes\n",
        "from pyscf import gto, scf, lo\n",
        "\n",
        "BOHR = 0.52917721092\n",
        "R = 1.8 * BOHR\n",
        "N = 6\n",
        "\n",
        "mol = gto.M(atom=[['H', (i * R, 0, 0)] for i in range(N)], basis=\"sto6g\", symmetry=\"c1\", verbose=0)\n",
        "mf = scf.RHF(mol).run(conv_tol=1E-14)\n",
        "\n",
        "mf.mo_coeff = lo.orth.lowdin(mol.intor('cint1e_ovlp_sph'))\n",
        "ncas, n_elec, spin, ecore, h1e, g2e, orb_sym = itg.get_rhf_integrals(mf, ncore=0, ncas=None, g2e_symm=8)\n",
        "\n",
        "driver = DMRGDriver(scratch=\"./tmp\", symm_type=SymmetryTypes.SU2, n_threads=4)\n",
        "driver.initialize_system(n_sites=ncas, n_elec=n_elec, spin=spin, orb_sym=orb_sym)\n",
        "\n",
        "bond_dims = [150] * 4 + [200] * 4\n",
        "noises = [1e-4] * 4 + [1e-5] * 4 + [0]\n",
        "thrds = [1e-10] * 8\n",
        "\n",
        "mpo = driver.get_qc_mpo(h1e=h1e, g2e=g2e, ecore=ecore, integral_cutoff=1E-8, iprint=1)\n",
        "ket = driver.get_random_mps(tag=\"KET\", bond_dim=150, nroots=1)\n",
        "energy = driver.dmrg(mpo, ket, n_sweeps=20, bond_dims=bond_dims, noises=noises,\n",
        "    thrds=thrds, iprint=1)\n",
        "print('Ground state energy = %20.15f' % energy)\n",
        "\n",
        "isite = 2\n",
        "mpo.const_e -= energy\n",
        "eta = 0.005\n",
        "\n",
        "dmpo = driver.get_site_mpo(op='D', site_index=isite, iprint=0)\n",
        "dket = driver.get_random_mps(tag=\"DKET\", bond_dim=200, center=ket.center, left_vacuum=dmpo.left_vacuum)\n",
        "driver.multiply(dket, dmpo, ket, n_sweeps=10, bond_dims=[200], thrds=[1E-10] * 10, iprint=1)\n",
        "\n",
        "freqs = np.arange(-0.8, -0.2, 0.01)\n",
        "gfmat = np.zeros((len(freqs), ), dtype=complex)\n",
        "for iw, freq in enumerate(freqs):\n",
        "    bra = driver.copy_mps(dket, tag=\"BRA\") # initial guess\n",
        "    gfmat[iw] = driver.greens_function(bra, mpo, dmpo, ket, freq, eta, n_sweeps=6,\n",
        "        bra_bond_dims=[200], ket_bond_dims=[200], thrds=[1E-6] * 10, iprint=0)\n",
        "    print(\"FREQ = %8.2f GF[%d,%d] = %12.6f + %12.6f i\" % (freq, isite, isite, gfmat[iw].real, gfmat[iw].imag))\n",
        "\n",
        "ldos = -1 / np.pi * gfmat.imag\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.grid(which='major', axis='both', alpha=0.5)\n",
        "plt.plot(freqs, ldos, linestyle='-', marker='o', markersize=4, mfc='white', mec=\"#7FB685\", color=\"#7FB685\")\n",
        "plt.xlabel(\"Frequency $\\\\omega$\")\n",
        "plt.ylabel(\"LDOS\")\n",
        "plt.show()"
      ],
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          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "oucBiDNpW_AZ",
        "outputId": "a46e8955-2378-462a-f639-e9d0d3394bba"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "integral symmetrize error =  0.0\n",
            "integral cutoff error =  0.0\n",
            "mpo terms =        863\n",
            "\n",
            "Build MPO | Nsites =     6 | Nterms =        863 | Algorithm = FastBIP | Cutoff = 1.00e-20\n",
            " Site =     0 /     6 .. Mmpo =    13 DW = 0.00e+00 NNZ =       13 SPT = 0.0000 Tmvc = 0.000 T = 0.008\n",
            " Site =     1 /     6 .. Mmpo =    34 DW = 0.00e+00 NNZ =      100 SPT = 0.7738 Tmvc = 0.000 T = 0.004\n",
            " Site =     2 /     6 .. Mmpo =    56 DW = 0.00e+00 NNZ =      185 SPT = 0.9028 Tmvc = 0.000 T = 0.004\n",
            " Site =     3 /     6 .. Mmpo =    34 DW = 0.00e+00 NNZ =      419 SPT = 0.7799 Tmvc = 0.001 T = 0.004\n",
            " Site =     4 /     6 .. Mmpo =    14 DW = 0.00e+00 NNZ =      105 SPT = 0.7794 Tmvc = 0.000 T = 0.003\n",
            " Site =     5 /     6 .. Mmpo =     1 DW = 0.00e+00 NNZ =       14 SPT = 0.0000 Tmvc = 0.000 T = 0.002\n",
            "Ttotal =      0.027 Tmvc-total = 0.002 MPO bond dimension =    56 MaxDW = 0.00e+00\n",
            "NNZ =          836 SIZE =         4753 SPT = 0.8241\n",
            "\n",
            "Rank =     0 Ttotal =      0.057 MPO method = FastBipartite bond dimension =      56 NNZ =          836 SIZE =         4753 SPT = 0.8241\n",
            "\n",
            "Sweep =    0 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.061 | E =      -3.2667431000 | DW = 1.41e-20\n",
            "\n",
            "Sweep =    1 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.105 | E =      -3.2667431000 | DE = 7.11e-15 | DW = 9.98e-21\n",
            "\n",
            "Sweep =    2 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.148 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 1.25e-20\n",
            "\n",
            "Sweep =    3 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.197 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 1.88e-20\n",
            "\n",
            "Sweep =    4 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.238 | E =      -3.2667431000 | DE = 1.78e-15 | DW = 1.13e-20\n",
            "\n",
            "Sweep =    5 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.280 | E =      -3.2667431000 | DE = 1.78e-15 | DW = 1.19e-20\n",
            "\n",
            "Sweep =    6 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.319 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 9.42e-21\n",
            "\n",
            "Sweep =    7 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.365 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 2.01e-20\n",
            "\n",
            "Sweep =    8 | Direction =  forward | Bond dimension =  200 | Noise =  0.00e+00 | Dav threshold =  1.00e-09\n",
            "Time elapsed =      0.400 | E =      -3.2667431000 | DE = 3.55e-15 | DW = 1.53e-20\n",
            "\n",
            "Ground state energy =   -3.266743099950662\n",
            "\n",
            "Sweep =    0 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.018 | F =    0.9962046481 | DW = 5.23e-25\n",
            "\n",
            "Sweep =    1 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.038 | F =    0.9970609307 | DF = 8.56e-04 | DW = 8.99e-25\n",
            "\n",
            "Sweep =    2 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.059 | F =    0.9970609307 | DF = 4.44e-16 | DW = 6.59e-25\n",
            "\n",
            "Sweep =    3 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.079 | F =    0.9970609307 | DF = -3.33e-16 | DW = 3.32e-25\n",
            "\n",
            "Sweep =    4 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.101 | F =    0.9970609307 | DF = -3.33e-16 | DW = 3.88e-25\n",
            "\n",
            "FREQ =    -0.80 GF[2,2] =    -2.858060 +    -0.132949 i\n",
            "FREQ =    -0.79 GF[2,2] =    -3.127639 +    -0.137862 i\n",
            "FREQ =    -0.78 GF[2,2] =    -3.410730 +    -0.146788 i\n",
            "FREQ =    -0.77 GF[2,2] =    -3.716042 +    -0.159910 i\n",
            "FREQ =    -0.76 GF[2,2] =    -4.052436 +    -0.177910 i\n",
            "FREQ =    -0.75 GF[2,2] =    -4.429247 +    -0.202036 i\n",
            "FREQ =    -0.74 GF[2,2] =    -4.862689 +    -0.234242 i\n",
            "FREQ =    -0.73 GF[2,2] =    -5.370446 +    -0.277828 i\n",
            "FREQ =    -0.72 GF[2,2] =    -5.979802 +    -0.338034 i\n",
            "FREQ =    -0.71 GF[2,2] =    -6.730787 +    -0.424057 i\n",
            "FREQ =    -0.70 GF[2,2] =    -7.689106 +    -0.552665 i\n",
            "FREQ =    -0.69 GF[2,2] =    -8.964426 +    -0.757635 i\n",
            "FREQ =    -0.68 GF[2,2] =   -10.763740 +    -1.118686 i\n",
            "FREQ =    -0.67 GF[2,2] =   -13.510429 +    -1.904433 i\n",
            "FREQ =    -0.66 GF[2,2] =   -17.418881 +    -3.612921 i\n",
            "FREQ =    -0.65 GF[2,2] =   -26.296063 +    -7.892317 i\n",
            "FREQ =    -0.64 GF[2,2] =   -44.979411 +   -35.247680 i\n",
            "FREQ =    -0.63 GF[2,2] =    41.659891 +   -56.954077 i\n",
            "FREQ =    -0.62 GF[2,2] =    27.132451 +   -10.471813 i\n",
            "FREQ =    -0.61 GF[2,2] =    16.312481 +    -3.861684 i\n",
            "FREQ =    -0.60 GF[2,2] =    11.092739 +    -2.003940 i\n",
            "FREQ =    -0.59 GF[2,2] =     8.036382 +    -1.254680 i\n",
            "FREQ =    -0.58 GF[2,2] =     5.972372 +    -0.893065 i\n",
            "FREQ =    -0.57 GF[2,2] =     4.418047 +    -0.708471 i\n",
            "FREQ =    -0.56 GF[2,2] =     3.108176 +    -0.629033 i\n",
            "FREQ =    -0.55 GF[2,2] =     1.874834 +    -0.643365 i\n",
            "FREQ =    -0.54 GF[2,2] =     0.501622 +    -0.805649 i\n",
            "FREQ =    -0.53 GF[2,2] =    -1.428740 +    -1.392787 i\n",
            "FREQ =    -0.52 GF[2,2] =    -5.038213 +    -4.367329 i\n",
            "FREQ =    -0.51 GF[2,2] =     5.385607 +   -16.985511 i\n",
            "FREQ =    -0.50 GF[2,2] =     8.132057 +    -3.176944 i\n",
            "FREQ =    -0.49 GF[2,2] =     5.112053 +    -1.122502 i\n",
            "FREQ =    -0.48 GF[2,2] =     3.547000 +    -0.626599 i\n",
            "FREQ =    -0.47 GF[2,2] =     2.530196 +    -0.443406 i\n",
            "FREQ =    -0.46 GF[2,2] =     1.745955 +    -0.363108 i\n",
            "FREQ =    -0.45 GF[2,2] =     1.066544 +    -0.329559 i\n",
            "FREQ =    -0.44 GF[2,2] =     0.421145 +    -0.324585 i\n",
            "FREQ =    -0.43 GF[2,2] =    -0.234970 +    -0.342450 i\n",
            "FREQ =    -0.42 GF[2,2] =    -0.955736 +    -0.386035 i\n",
            "FREQ =    -0.41 GF[2,2] =    -1.792136 +    -0.464805 i\n",
            "FREQ =    -0.40 GF[2,2] =    -2.833594 +    -0.601140 i\n",
            "FREQ =    -0.39 GF[2,2] =    -4.230434 +    -0.846750 i\n",
            "FREQ =    -0.38 GF[2,2] =    -6.289553 +    -1.335939 i\n",
            "FREQ =    -0.37 GF[2,2] =    -9.737590 +    -2.501588 i\n",
            "FREQ =    -0.36 GF[2,2] =   -16.688375 +    -6.387690 i\n",
            "FREQ =    -0.35 GF[2,2] =   -29.656382 +   -31.528685 i\n",
            "FREQ =    -0.34 GF[2,2] =    34.225016 +   -32.546412 i\n",
            "FREQ =    -0.33 GF[2,2] =    21.430321 +    -6.498027 i\n",
            "FREQ =    -0.32 GF[2,2] =    14.419157 +    -2.511719 i\n",
            "FREQ =    -0.31 GF[2,2] =    10.986939 +    -1.318801 i\n",
            "FREQ =    -0.30 GF[2,2] =     8.980094 +    -0.814240 i\n",
            "FREQ =    -0.29 GF[2,2] =     7.662527 +    -0.555185 i\n",
            "FREQ =    -0.28 GF[2,2] =     6.728338 +    -0.404730 i\n",
            "FREQ =    -0.27 GF[2,2] =     6.027647 +    -0.309463 i\n",
            "FREQ =    -0.26 GF[2,2] =     5.481284 +    -0.245307 i\n",
            "FREQ =    -0.25 GF[2,2] =     5.041000 +    -0.199912 i\n",
            "FREQ =    -0.24 GF[2,2] =     4.677884 +    -0.166589 i\n",
            "FREQ =    -0.23 GF[2,2] =     4.372155 +    -0.141336 i\n",
            "FREQ =    -0.22 GF[2,2] =     4.110743 +    -0.121720 i\n",
            "FREQ =    -0.21 GF[2,2] =     3.883890 +    -0.106156 i\n",
            "FREQ =    -0.20 GF[2,2] =     3.685138 +    -0.093570 i\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the ``SZ`` mode:"
      ],
      "metadata": {
        "id": "8SP4zRQCW-pH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from pyblock2._pyscf.ao2mo import integrals as itg\n",
        "from pyblock2.driver.core import DMRGDriver, SymmetryTypes\n",
        "from pyscf import gto, scf, lo\n",
        "\n",
        "BOHR = 0.52917721092\n",
        "R = 1.8 * BOHR\n",
        "N = 6\n",
        "\n",
        "mol = gto.M(atom=[['H', (i * R, 0, 0)] for i in range(N)], basis=\"sto6g\", symmetry=\"c1\", verbose=0)\n",
        "mf = scf.RHF(mol).run(conv_tol=1E-14)\n",
        "\n",
        "mf.mo_coeff = lo.orth.lowdin(mol.intor('cint1e_ovlp_sph'))\n",
        "ncas, n_elec, spin, ecore, h1e, g2e, orb_sym = itg.get_rhf_integrals(mf, ncore=0, ncas=None, g2e_symm=8)\n",
        "\n",
        "driver = DMRGDriver(scratch=\"./tmp\", symm_type=SymmetryTypes.SZ, n_threads=4)\n",
        "driver.initialize_system(n_sites=ncas, n_elec=n_elec, spin=spin, orb_sym=orb_sym)\n",
        "\n",
        "bond_dims = [150] * 4 + [200] * 4\n",
        "noises = [1e-4] * 4 + [1e-5] * 4 + [0]\n",
        "thrds = [1e-10] * 8\n",
        "\n",
        "mpo = driver.get_qc_mpo(h1e=h1e, g2e=g2e, ecore=ecore, integral_cutoff=1E-8, iprint=1)\n",
        "ket = driver.get_random_mps(tag=\"KET\", bond_dim=150, nroots=1)\n",
        "energy = driver.dmrg(mpo, ket, n_sweeps=20, bond_dims=bond_dims, noises=noises,\n",
        "    thrds=thrds, iprint=1)\n",
        "print('Ground state energy = %20.15f' % energy)\n",
        "\n",
        "isite = 2\n",
        "mpo.const_e -= energy\n",
        "eta = 0.005\n",
        "\n",
        "dmpo = driver.get_site_mpo(op='d', site_index=isite, iprint=0) # only alpha spin\n",
        "dket = driver.get_random_mps(tag=\"DKET\", bond_dim=200, center=ket.center, target=dmpo.op.q_label + ket.info.target)\n",
        "driver.multiply(dket, dmpo, ket, n_sweeps=10, bond_dims=[200], thrds=[1E-10] * 10, iprint=1)\n",
        "\n",
        "freqs = np.arange(-0.8, -0.2, 0.01)\n",
        "gfmat = np.zeros((len(freqs), ), dtype=complex)\n",
        "for iw, freq in enumerate(freqs):\n",
        "    bra = driver.copy_mps(dket, tag=\"BRA\") # initial guess\n",
        "    gfmat[iw] = driver.greens_function(bra, mpo, dmpo, ket, freq, eta, n_sweeps=6,\n",
        "        bra_bond_dims=[200], ket_bond_dims=[200], thrds=[1E-6] * 10, iprint=0)\n",
        "    print(\"FREQ = %8.2f GF[%d,%d] = %12.6f + %12.6f i\" % (freq, isite, isite, gfmat[iw].real, gfmat[iw].imag))\n",
        "\n",
        "ldos = -2 / np.pi * gfmat.imag # account for both spin\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.grid(which='major', axis='both', alpha=0.5)\n",
        "plt.plot(freqs, ldos, linestyle='-', marker='o', markersize=4, mfc='white', mec=\"#7FB685\", color=\"#7FB685\")\n",
        "plt.xlabel(\"Frequency $\\\\omega$\")\n",
        "plt.ylabel(\"LDOS\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "j54bhPXwXWwi",
        "outputId": "1cddb32f-2edb-4095-cc5c-4267c513f21f"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "integral symmetrize error =  0.0\n",
            "integral cutoff error =  0.0\n",
            "mpo terms =       2286\n",
            "\n",
            "Build MPO | Nsites =     6 | Nterms =       2286 | Algorithm = FastBIP | Cutoff = 1.00e-20\n",
            " Site =     0 /     6 .. Mmpo =    26 DW = 0.00e+00 NNZ =       26 SPT = 0.0000 Tmvc = 0.001 T = 0.008\n",
            " Site =     1 /     6 .. Mmpo =    66 DW = 0.00e+00 NNZ =      243 SPT = 0.8584 Tmvc = 0.001 T = 0.011\n",
            " Site =     2 /     6 .. Mmpo =   110 DW = 0.00e+00 NNZ =      459 SPT = 0.9368 Tmvc = 0.002 T = 0.009\n",
            " Site =     3 /     6 .. Mmpo =    66 DW = 0.00e+00 NNZ =     1147 SPT = 0.8420 Tmvc = 0.001 T = 0.016\n",
            " Site =     4 /     6 .. Mmpo =    26 DW = 0.00e+00 NNZ =      243 SPT = 0.8584 Tmvc = 0.000 T = 0.006\n",
            " Site =     5 /     6 .. Mmpo =     1 DW = 0.00e+00 NNZ =       26 SPT = 0.0000 Tmvc = 0.000 T = 0.008\n",
            "Ttotal =      0.057 Tmvc-total = 0.005 MPO bond dimension =   110 MaxDW = 0.00e+00\n",
            "NNZ =         2144 SIZE =        18004 SPT = 0.8809\n",
            "\n",
            "Rank =     0 Ttotal =      0.097 MPO method = FastBipartite bond dimension =     110 NNZ =         2144 SIZE =        18004 SPT = 0.8809\n",
            "\n",
            "Sweep =    0 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.168 | E =      -3.2667431000 | DW = 1.33e-20\n",
            "\n",
            "Sweep =    1 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.305 | E =      -3.2667431000 | DE = -7.11e-15 | DW = 1.29e-20\n",
            "\n",
            "Sweep =    2 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.432 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 2.12e-20\n",
            "\n",
            "Sweep =    3 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.557 | E =      -3.2667431000 | DE = 3.55e-15 | DW = 1.89e-20\n",
            "\n",
            "Sweep =    4 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.678 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 1.98e-20\n",
            "\n",
            "Sweep =    5 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.811 | E =      -3.2667431000 | DE = -5.33e-15 | DW = 3.57e-20\n",
            "\n",
            "Sweep =    6 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.935 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 1.87e-20\n",
            "\n",
            "Sweep =    7 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      1.070 | E =      -3.2667431000 | DE = 7.11e-15 | DW = 1.72e-20\n",
            "\n",
            "Sweep =    8 | Direction =  forward | Bond dimension =  200 | Noise =  0.00e+00 | Dav threshold =  1.00e-09\n",
            "Time elapsed =      1.172 | E =      -3.2667431000 | DE = -5.33e-15 | DW = 4.35e-20\n",
            "\n",
            "Ground state energy =   -3.266743099973319\n",
            "\n",
            "Sweep =    0 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.019 | F =    0.6660221816 | DW = 9.82e-26\n",
            "\n",
            "Sweep =    1 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.042 | F =    0.7050281723 | DF = 3.90e-02 | DW = 1.70e-24\n",
            "\n",
            "Sweep =    2 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.063 | F =    0.7050281723 | DF = 6.66e-16 | DW = 2.63e-25\n",
            "\n",
            "Sweep =    3 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.084 | F =    0.7050281723 | DF = 3.33e-16 | DW = 1.94e-24\n",
            "\n",
            "Sweep =    4 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.105 | F =    0.7050281723 | DF = 1.11e-16 | DW = 8.09e-25\n",
            "\n",
            "FREQ =    -0.80 GF[2,2] =    -1.429314 +    -0.066472 i\n",
            "FREQ =    -0.79 GF[2,2] =    -1.563695 +    -0.068960 i\n",
            "FREQ =    -0.78 GF[2,2] =    -1.705301 +    -0.073389 i\n",
            "FREQ =    -0.77 GF[2,2] =    -1.857857 +    -0.079957 i\n",
            "FREQ =    -0.76 GF[2,2] =    -2.026014 +    -0.088950 i\n",
            "FREQ =    -0.75 GF[2,2] =    -2.215113 +    -0.101005 i\n",
            "FREQ =    -0.74 GF[2,2] =    -2.431836 +    -0.117119 i\n",
            "FREQ =    -0.73 GF[2,2] =    -2.685052 +    -0.138881 i\n",
            "FREQ =    -0.72 GF[2,2] =    -2.989529 +    -0.168989 i\n",
            "FREQ =    -0.71 GF[2,2] =    -3.364958 +    -0.212001 i\n",
            "FREQ =    -0.70 GF[2,2] =    -3.843595 +    -0.276232 i\n",
            "FREQ =    -0.69 GF[2,2] =    -4.481702 +    -0.378669 i\n",
            "FREQ =    -0.68 GF[2,2] =    -5.379774 +    -0.559234 i\n",
            "FREQ =    -0.67 GF[2,2] =    -6.754026 +    -0.952219 i\n",
            "FREQ =    -0.66 GF[2,2] =    -8.711280 +    -1.806963 i\n",
            "FREQ =    -0.65 GF[2,2] =   -13.147719 +    -3.946547 i\n",
            "FREQ =    -0.64 GF[2,2] =   -22.488537 +   -17.623137 i\n",
            "FREQ =    -0.63 GF[2,2] =    20.830470 +   -28.478123 i\n",
            "FREQ =    -0.62 GF[2,2] =    13.568650 +    -5.237022 i\n",
            "FREQ =    -0.61 GF[2,2] =     8.158524 +    -1.931326 i\n",
            "FREQ =    -0.60 GF[2,2] =     5.546668 +    -1.001994 i\n",
            "FREQ =    -0.59 GF[2,2] =     4.015779 +    -0.627121 i\n",
            "FREQ =    -0.58 GF[2,2] =     2.986254 +    -0.446332 i\n",
            "FREQ =    -0.57 GF[2,2] =     2.206705 +    -0.354016 i\n",
            "FREQ =    -0.56 GF[2,2] =     1.553827 +    -0.314387 i\n",
            "FREQ =    -0.55 GF[2,2] =     0.934667 +    -0.321487 i\n",
            "FREQ =    -0.54 GF[2,2] =     0.247498 +    -0.402597 i\n",
            "FREQ =    -0.53 GF[2,2] =    -0.716559 +    -0.696260 i\n",
            "FREQ =    -0.52 GF[2,2] =    -2.517667 +    -2.183247 i\n",
            "FREQ =    -0.51 GF[2,2] =     2.694685 +    -8.495055 i\n",
            "FREQ =    -0.50 GF[2,2] =     4.068420 +    -1.589597 i\n",
            "FREQ =    -0.49 GF[2,2] =     2.556421 +    -0.561628 i\n",
            "FREQ =    -0.48 GF[2,2] =     1.776438 +    -0.313770 i\n",
            "FREQ =    -0.47 GF[2,2] =     1.266039 +    -0.222005 i\n",
            "FREQ =    -0.46 GF[2,2] =     0.873240 +    -0.181737 i\n",
            "FREQ =    -0.45 GF[2,2] =     0.533170 +    -0.164892 i\n",
            "FREQ =    -0.44 GF[2,2] =     0.210275 +    -0.162307 i\n",
            "FREQ =    -0.43 GF[2,2] =    -0.119248 +    -0.171350 i\n",
            "FREQ =    -0.42 GF[2,2] =    -0.478803 +    -0.193119 i\n",
            "FREQ =    -0.41 GF[2,2] =    -0.898305 +    -0.232404 i\n",
            "FREQ =    -0.40 GF[2,2] =    -1.418566 +    -0.300549 i\n",
            "FREQ =    -0.39 GF[2,2] =    -2.115432 +    -0.423477 i\n",
            "FREQ =    -0.38 GF[2,2] =    -3.145615 +    -0.668038 i\n",
            "FREQ =    -0.37 GF[2,2] =    -4.871226 +    -1.251034 i\n",
            "FREQ =    -0.36 GF[2,2] =    -8.345991 +    -3.194131 i\n",
            "FREQ =    -0.35 GF[2,2] =   -14.828832 +   -15.765406 i\n",
            "FREQ =    -0.34 GF[2,2] =    17.111094 +   -16.271567 i\n",
            "FREQ =    -0.33 GF[2,2] =    10.713170 +    -3.248626 i\n",
            "FREQ =    -0.32 GF[2,2] =     7.207938 +    -1.255671 i\n",
            "FREQ =    -0.31 GF[2,2] =     5.490817 +    -0.659108 i\n",
            "FREQ =    -0.30 GF[2,2] =     4.488220 +    -0.406981 i\n",
            "FREQ =    -0.29 GF[2,2] =     3.829440 +    -0.277473 i\n",
            "FREQ =    -0.28 GF[2,2] =     3.362384 +    -0.202273 i\n",
            "FREQ =    -0.27 GF[2,2] =     3.011931 +    -0.154637 i\n",
            "FREQ =    -0.26 GF[2,2] =     2.738941 +    -0.122582 i\n",
            "FREQ =    -0.25 GF[2,2] =     2.518611 +    -0.099880 i\n",
            "FREQ =    -0.24 GF[2,2] =     2.336457 +    -0.083188 i\n",
            "FREQ =    -0.23 GF[2,2] =     2.183385 +    -0.070557 i\n",
            "FREQ =    -0.22 GF[2,2] =     2.053131 +    -0.060779 i\n",
            "FREQ =    -0.21 GF[2,2] =     1.939693 +    -0.052990 i\n",
            "FREQ =    -0.20 GF[2,2] =     1.840458 +    -0.046715 i\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Time-Dependent DMRG\n",
        "\n",
        "Here we use real time TD-DMRG and Fast Fourier Transform (FFT) to calculate the Green's function.\n",
        "\n",
        "This is obtained from a Fourier transform from time domain to frequency domain:\n",
        "\n",
        "$$\n",
        "    G_{ij}(t) = - i \\langle \\Psi_0 | a_j^\\dagger \\mathrm{e}^{-i (\\hat{H}_0 - E_0 ) t} a_i |\\Psi_0\\rangle \\\\\n",
        "    G_{ij}(\\omega) = \\int_{-\\infty}^{\\infty} \\mathrm{d} t \\mathrm{e}^{-i \\omega t} G_{ij}(t) \\mathrm{e}^{- \\eta t}\n",
        "$$\n",
        "\n",
        "where $\\mathrm{e}^{- \\eta t}$ is a broading factor.\n",
        "\n",
        "In the ``SU2`` mode:"
      ],
      "metadata": {
        "id": "U9vVZiCMXh7U"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "iIApuO0PUuSP",
        "outputId": "301d6a4c-ab64-452c-980b-b97fdfdc0f27"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "integral symmetrize error =  0.0\n",
            "integral cutoff error =  0.0\n",
            "mpo terms =        863\n",
            "\n",
            "Build MPO | Nsites =     6 | Nterms =        863 | Algorithm = FastBIP | Cutoff = 1.00e-20\n",
            " Site =     0 /     6 .. Mmpo =    13 DW = 0.00e+00 NNZ =       13 SPT = 0.0000 Tmvc = 0.000 T = 0.014\n",
            " Site =     1 /     6 .. Mmpo =    34 DW = 0.00e+00 NNZ =      100 SPT = 0.7738 Tmvc = 0.000 T = 0.008\n",
            " Site =     2 /     6 .. Mmpo =    56 DW = 0.00e+00 NNZ =      185 SPT = 0.9028 Tmvc = 0.000 T = 0.008\n",
            " Site =     3 /     6 .. Mmpo =    34 DW = 0.00e+00 NNZ =      419 SPT = 0.7799 Tmvc = 0.000 T = 0.016\n",
            " Site =     4 /     6 .. Mmpo =    14 DW = 0.00e+00 NNZ =      105 SPT = 0.7794 Tmvc = 0.000 T = 0.013\n",
            " Site =     5 /     6 .. Mmpo =     1 DW = 0.00e+00 NNZ =       14 SPT = 0.0000 Tmvc = 0.001 T = 0.027\n",
            "Ttotal =      0.087 Tmvc-total = 0.002 MPO bond dimension =    56 MaxDW = 0.00e+00\n",
            "NNZ =          836 SIZE =         4753 SPT = 0.8241\n",
            "\n",
            "Rank =     0 Ttotal =      0.190 MPO method = FastBipartite bond dimension =      56 NNZ =          836 SIZE =         4753 SPT = 0.8241\n",
            "\n",
            "Sweep =    0 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.138 | E =      -3.2667431000 | DW = 5.73e-21\n",
            "\n",
            "Sweep =    1 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.227 | E =      -3.2667431000 | DE = 4.09e-14 | DW = 1.64e-20\n",
            "\n",
            "Sweep =    2 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.327 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 9.52e-21\n",
            "\n",
            "Sweep =    3 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.428 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 1.55e-20\n",
            "\n",
            "Sweep =    4 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.521 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 6.12e-21\n",
            "\n",
            "Sweep =    5 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.634 | E =      -3.2667431000 | DE = -3.55e-15 | DW = 2.47e-20\n",
            "\n",
            "Sweep =    6 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.781 | E =      -3.2667431000 | DE = 7.11e-15 | DW = 7.01e-21\n",
            "\n",
            "Sweep =    7 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.876 | E =      -3.2667431000 | DE = 1.78e-15 | DW = 1.12e-20\n",
            "\n",
            "Sweep =    8 | Direction =  forward | Bond dimension =  200 | Noise =  0.00e+00 | Dav threshold =  1.00e-09\n",
            "Time elapsed =      0.997 | E =      -3.2667431000 | DE = 1.78e-15 | DW = 1.93e-20\n",
            "\n",
            "Ground state energy =   -3.266743099951065\n",
            "\n",
            "Sweep =    0 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.057 | F = (0.9960879032,0.0000000000) | DW = 3.05e-25\n",
            "\n",
            "Sweep =    1 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.120 | F = (0.9970594762,0.0000000000) | DF = (9.72e-04,0.00e+00) | DW = 9.73e-25\n",
            "\n",
            "Sweep =    2 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.168 | F = (0.9970594762,0.0000000000) | DF = (4.44e-16,0.00e+00) | DW = 1.57e-25\n",
            "\n",
            "Sweep =    3 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.213 | F = (0.9970594762,0.0000000000) | DF = (-5.55e-16,0.00e+00) | DW = 3.36e-25\n",
            "\n",
            "Sweep =    4 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.262 | F = (0.9970594762,0.0000000000) | DF = (2.22e-16,0.00e+00) | DW = 1.04e-24\n",
            "\n",
            "it =     0 ( 0.0 %)\n",
            "it =    25 ( 1.0 %)\n",
            "it =    50 ( 2.0 %)\n",
            "it =    75 ( 3.0 %)\n",
            "it =   100 ( 4.0 %)\n",
            "it =   125 ( 5.0 %)\n",
            "it =   150 ( 6.0 %)\n",
            "it =   175 ( 7.0 %)\n",
            "it =   200 ( 8.0 %)\n",
            "it =   225 ( 9.0 %)\n",
            "it =   250 (10.0 %)\n",
            "it =   275 (11.0 %)\n",
            "it =   300 (12.0 %)\n",
            "it =   325 (13.0 %)\n",
            "it =   350 (14.0 %)\n",
            "it =   375 (15.0 %)\n",
            "it =   400 (16.0 %)\n",
            "it =   425 (17.0 %)\n",
            "it =   450 (18.0 %)\n",
            "it =   475 (19.0 %)\n",
            "it =   500 (20.0 %)\n",
            "it =   525 (21.0 %)\n",
            "it =   550 (22.0 %)\n",
            "it =   575 (23.0 %)\n",
            "it =   600 (24.0 %)\n",
            "it =   625 (25.0 %)\n",
            "it =   650 (26.0 %)\n",
            "it =   675 (27.0 %)\n",
            "it =   700 (28.0 %)\n",
            "it =   725 (29.0 %)\n",
            "it =   750 (30.0 %)\n",
            "it =   775 (31.0 %)\n",
            "it =   800 (32.0 %)\n",
            "it =   825 (33.0 %)\n",
            "it =   850 (34.0 %)\n",
            "it =   875 (35.0 %)\n",
            "it =   900 (36.0 %)\n",
            "it =   925 (37.0 %)\n",
            "it =   950 (38.0 %)\n",
            "it =   975 (39.0 %)\n",
            "it =  1000 (40.0 %)\n",
            "it =  1025 (41.0 %)\n",
            "it =  1050 (42.0 %)\n",
            "it =  1075 (43.0 %)\n",
            "it =  1100 (44.0 %)\n",
            "it =  1125 (45.0 %)\n",
            "it =  1150 (46.0 %)\n",
            "it =  1175 (47.0 %)\n",
            "it =  1200 (48.0 %)\n",
            "it =  1225 (49.0 %)\n",
            "it =  1250 (50.0 %)\n",
            "it =  1275 (51.0 %)\n",
            "it =  1300 (52.0 %)\n",
            "it =  1325 (53.0 %)\n",
            "it =  1350 (54.0 %)\n",
            "it =  1375 (55.0 %)\n",
            "it =  1400 (56.0 %)\n",
            "it =  1425 (57.0 %)\n",
            "it =  1450 (58.0 %)\n",
            "it =  1475 (59.0 %)\n",
            "it =  1500 (60.0 %)\n",
            "it =  1525 (61.0 %)\n",
            "it =  1550 (62.0 %)\n",
            "it =  1575 (63.0 %)\n",
            "it =  1600 (64.0 %)\n",
            "it =  1625 (65.0 %)\n",
            "it =  1650 (66.0 %)\n",
            "it =  1675 (67.0 %)\n",
            "it =  1700 (68.0 %)\n",
            "it =  1725 (69.0 %)\n",
            "it =  1750 (70.0 %)\n",
            "it =  1775 (71.0 %)\n",
            "it =  1800 (72.0 %)\n",
            "it =  1825 (73.0 %)\n",
            "it =  1850 (74.0 %)\n",
            "it =  1875 (75.0 %)\n",
            "it =  1900 (76.0 %)\n",
            "it =  1925 (77.0 %)\n",
            "it =  1950 (78.0 %)\n",
            "it =  1975 (79.0 %)\n",
            "it =  2000 (80.0 %)\n",
            "it =  2025 (81.0 %)\n",
            "it =  2050 (82.0 %)\n",
            "it =  2075 (83.0 %)\n",
            "it =  2100 (84.0 %)\n",
            "it =  2125 (85.0 %)\n",
            "it =  2150 (86.0 %)\n",
            "it =  2175 (87.0 %)\n",
            "it =  2200 (88.0 %)\n",
            "it =  2225 (89.0 %)\n",
            "it =  2250 (90.0 %)\n",
            "it =  2275 (91.0 %)\n",
            "it =  2300 (92.0 %)\n",
            "it =  2325 (93.0 %)\n",
            "it =  2350 (94.0 %)\n",
            "it =  2375 (95.0 %)\n",
            "it =  2400 (96.0 %)\n",
            "it =  2425 (97.0 %)\n",
            "it =  2450 (98.0 %)\n",
            "it =  2475 (99.0 %)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "from pyblock2._pyscf.ao2mo import integrals as itg\n",
        "from pyblock2.driver.core import DMRGDriver, SymmetryTypes\n",
        "from pyscf import gto, scf, lo\n",
        "\n",
        "BOHR = 0.52917721092\n",
        "R = 1.8 * BOHR\n",
        "N = 6\n",
        "\n",
        "mol = gto.M(atom=[['H', (i * R, 0, 0)] for i in range(N)], basis=\"sto6g\", symmetry=\"c1\", verbose=0)\n",
        "mf = scf.RHF(mol).run(conv_tol=1E-14)\n",
        "\n",
        "mf.mo_coeff = lo.orth.lowdin(mol.intor('cint1e_ovlp_sph'))\n",
        "ncas, n_elec, spin, ecore, h1e, g2e, orb_sym = itg.get_rhf_integrals(mf, ncore=0, ncas=None, g2e_symm=8)\n",
        "\n",
        "driver = DMRGDriver(scratch=\"./tmp\", symm_type=SymmetryTypes.SU2 | SymmetryTypes.CPX, n_threads=4)\n",
        "driver.initialize_system(n_sites=ncas, n_elec=n_elec, spin=spin, orb_sym=orb_sym)\n",
        "\n",
        "bond_dims = [150] * 4 + [200] * 4\n",
        "noises = [1e-4] * 4 + [1e-5] * 4 + [0]\n",
        "thrds = [1e-10] * 8\n",
        "\n",
        "mpo = driver.get_qc_mpo(h1e=h1e, g2e=g2e, ecore=ecore, integral_cutoff=1E-8, iprint=1)\n",
        "ket = driver.get_random_mps(tag=\"KET\", bond_dim=150, nroots=1)\n",
        "energy = driver.dmrg(mpo, ket, n_sweeps=20, bond_dims=bond_dims, noises=noises,\n",
        "    thrds=thrds, iprint=1)\n",
        "print('Ground state energy = %20.15f' % energy)\n",
        "\n",
        "isite = 2\n",
        "mpo.const_e -= energy\n",
        "eta = 0.005\n",
        "\n",
        "dmpo = driver.get_site_mpo(op='D', site_index=isite, iprint=0)\n",
        "dket = driver.get_random_mps(tag=\"DKET\", bond_dim=200, center=ket.center, left_vacuum=dmpo.left_vacuum)\n",
        "driver.multiply(dket, dmpo, ket, n_sweeps=10, bond_dims=[200], thrds=[1E-10] * 10, iprint=1)\n",
        "\n",
        "impo = driver.get_identity_mpo()\n",
        "dbra = driver.copy_mps(dket, tag='DBRA')\n",
        "\n",
        "dt = 0.2\n",
        "t = 500.0\n",
        "nstep = int(t / dt)\n",
        "rtgf = np.zeros((nstep, ), dtype=complex)\n",
        "rtgf[0] = driver.expectation(dket, impo, dket)\n",
        "for it in range(nstep - 1):\n",
        "    if it % (nstep // 100) == 0:\n",
        "        print(\"it = %5d (%4.1f %%)\" % (it, it * 100 / nstep))\n",
        "    dbra = driver.td_dmrg(mpo, dbra, -dt * 1j, -dt * 1j, final_mps_tag='DBRA', hermitian=True, bond_dims=[200], iprint=0)\n",
        "    rtgf[it + 1] = driver.expectation(dbra, impo, dket)\n",
        "\n",
        "def gf_fft(eta, dt, rtgf, npts):\n",
        "    frq = np.fft.fftfreq(npts, dt)\n",
        "    frq = np.fft.fftshift(frq) * 2.0 * np.pi\n",
        "    fftinp = -1j * rtgf * np.exp(-eta * dt * np.arange(0, npts))\n",
        "    return frq, np.fft.fftshift(np.fft.fft(fftinp)) * dt\n",
        "\n",
        "frq, frq_gf = gf_fft(eta, dt, rtgf, len(rtgf))\n",
        "frq_gf = frq_gf[(frq >= -0.8) & (frq < -0.2)]\n",
        "frq = frq[(frq >= -0.8) & (frq < -0.2)]\n",
        "\n",
        "ldos = -1 / np.pi * frq_gf.imag\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.grid(which='major', axis='both', alpha=0.5)\n",
        "plt.plot(frq, ldos, linestyle='-', marker='o', markersize=4, mfc='white', mec=\"#7FB685\", color=\"#7FB685\")\n",
        "plt.xlabel(\"Frequency $\\\\omega$\")\n",
        "plt.ylabel(\"LDOS\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the ``SZ`` mode:"
      ],
      "metadata": {
        "id": "Y8PJt9kuYT3o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from pyblock2._pyscf.ao2mo import integrals as itg\n",
        "from pyblock2.driver.core import DMRGDriver, SymmetryTypes\n",
        "from pyscf import gto, scf, lo\n",
        "\n",
        "BOHR = 0.52917721092\n",
        "R = 1.8 * BOHR\n",
        "N = 6\n",
        "\n",
        "mol = gto.M(atom=[['H', (i * R, 0, 0)] for i in range(N)], basis=\"sto6g\", symmetry=\"c1\", verbose=0)\n",
        "mf = scf.RHF(mol).run(conv_tol=1E-14)\n",
        "\n",
        "mf.mo_coeff = lo.orth.lowdin(mol.intor('cint1e_ovlp_sph'))\n",
        "ncas, n_elec, spin, ecore, h1e, g2e, orb_sym = itg.get_rhf_integrals(mf, ncore=0, ncas=None, g2e_symm=8)\n",
        "\n",
        "driver = DMRGDriver(scratch=\"./tmp\", symm_type=SymmetryTypes.SZ | SymmetryTypes.CPX, n_threads=4)\n",
        "driver.initialize_system(n_sites=ncas, n_elec=n_elec, spin=spin, orb_sym=orb_sym)\n",
        "\n",
        "bond_dims = [150] * 4 + [200] * 4\n",
        "noises = [1e-4] * 4 + [1e-5] * 4 + [0]\n",
        "thrds = [1e-10] * 8\n",
        "\n",
        "mpo = driver.get_qc_mpo(h1e=h1e, g2e=g2e, ecore=ecore, integral_cutoff=1E-8, iprint=1)\n",
        "ket = driver.get_random_mps(tag=\"KET\", bond_dim=150, nroots=1)\n",
        "energy = driver.dmrg(mpo, ket, n_sweeps=20, bond_dims=bond_dims, noises=noises,\n",
        "    thrds=thrds, iprint=1)\n",
        "print('Ground state energy = %20.15f' % energy)\n",
        "\n",
        "isite = 2\n",
        "mpo.const_e -= energy\n",
        "eta = 0.005\n",
        "\n",
        "dmpo = driver.get_site_mpo(op='d', site_index=isite, iprint=0) # only alpha spin\n",
        "dket = driver.get_random_mps(tag=\"DKET\", bond_dim=200, center=ket.center, target=dmpo.op.q_label + ket.info.target)\n",
        "driver.multiply(dket, dmpo, ket, n_sweeps=10, bond_dims=[200], thrds=[1E-10] * 10, iprint=1)\n",
        "\n",
        "impo = driver.get_identity_mpo()\n",
        "dbra = driver.copy_mps(dket, tag='DBRA')\n",
        "\n",
        "dt = 0.2\n",
        "t = 500.0\n",
        "nstep = int(t / dt)\n",
        "rtgf = np.zeros((nstep, ), dtype=complex)\n",
        "rtgf[0] = driver.expectation(dket, impo, dket)\n",
        "for it in range(nstep - 1):\n",
        "    if it % (nstep // 100) == 0:\n",
        "        print(\"it = %5d (%4.1f %%)\" % (it, it * 100 / nstep))\n",
        "    dbra = driver.td_dmrg(mpo, dbra, -dt * 1j, -dt * 1j, final_mps_tag='DBRA', hermitian=True, bond_dims=[200], iprint=0)\n",
        "    rtgf[it + 1] = driver.expectation(dbra, impo, dket)\n",
        "\n",
        "def gf_fft(eta, dt, rtgf, npts):\n",
        "    frq = np.fft.fftfreq(npts, dt)\n",
        "    frq = np.fft.fftshift(frq) * 2.0 * np.pi\n",
        "    fftinp = -1j * rtgf * np.exp(-eta * dt * np.arange(0, npts))\n",
        "    return frq, np.fft.fftshift(np.fft.fft(fftinp)) * dt\n",
        "\n",
        "frq, frq_gf = gf_fft(eta, dt, rtgf, len(rtgf))\n",
        "frq_gf = frq_gf[(frq >= -0.8) & (frq < -0.2)]\n",
        "frq = frq[(frq >= -0.8) & (frq < -0.2)]\n",
        "\n",
        "ldos = -2 / np.pi * frq_gf.imag\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.grid(which='major', axis='both', alpha=0.5)\n",
        "plt.plot(frq, ldos, linestyle='-', marker='o', markersize=4, mfc='white', mec=\"#7FB685\", color=\"#7FB685\")\n",
        "plt.xlabel(\"Frequency $\\\\omega$\")\n",
        "plt.ylabel(\"LDOS\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "xD9qDnvtYUyv",
        "outputId": "90677109-c9ea-4175-ed8b-1e94a54eb35a"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "integral symmetrize error =  0.0\n",
            "integral cutoff error =  0.0\n",
            "mpo terms =       2286\n",
            "\n",
            "Build MPO | Nsites =     6 | Nterms =       2286 | Algorithm = FastBIP | Cutoff = 1.00e-20\n",
            " Site =     0 /     6 .. Mmpo =    26 DW = 0.00e+00 NNZ =       26 SPT = 0.0000 Tmvc = 0.001 T = 0.016\n",
            " Site =     1 /     6 .. Mmpo =    66 DW = 0.00e+00 NNZ =      243 SPT = 0.8584 Tmvc = 0.001 T = 0.016\n",
            " Site =     2 /     6 .. Mmpo =   110 DW = 0.00e+00 NNZ =      459 SPT = 0.9368 Tmvc = 0.001 T = 0.014\n",
            " Site =     3 /     6 .. Mmpo =    66 DW = 0.00e+00 NNZ =     1147 SPT = 0.8420 Tmvc = 0.001 T = 0.013\n",
            " Site =     4 /     6 .. Mmpo =    26 DW = 0.00e+00 NNZ =      243 SPT = 0.8584 Tmvc = 0.000 T = 0.004\n",
            " Site =     5 /     6 .. Mmpo =     1 DW = 0.00e+00 NNZ =       26 SPT = 0.0000 Tmvc = 0.000 T = 0.003\n",
            "Ttotal =      0.066 Tmvc-total = 0.004 MPO bond dimension =   110 MaxDW = 0.00e+00\n",
            "NNZ =         2144 SIZE =        18004 SPT = 0.8809\n",
            "\n",
            "Rank =     0 Ttotal =      0.124 MPO method = FastBipartite bond dimension =     110 NNZ =         2144 SIZE =        18004 SPT = 0.8809\n",
            "\n",
            "Sweep =    0 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.230 | E =      -3.2667431000 | DW = 7.12e-17\n",
            "\n",
            "Sweep =    1 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.413 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 6.71e-17\n",
            "\n",
            "Sweep =    2 | Direction =  forward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.563 | E =      -3.2667431000 | DE = 3.55e-15 | DW = 6.86e-17\n",
            "\n",
            "Sweep =    3 | Direction = backward | Bond dimension =  150 | Noise =  1.00e-04 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.770 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 7.22e-17\n",
            "\n",
            "Sweep =    4 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      0.951 | E =      -3.2667431000 | DE = -3.55e-15 | DW = 1.68e-20\n",
            "\n",
            "Sweep =    5 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      1.109 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 2.60e-20\n",
            "\n",
            "Sweep =    6 | Direction =  forward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      1.261 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 1.87e-20\n",
            "\n",
            "Sweep =    7 | Direction = backward | Bond dimension =  200 | Noise =  1.00e-05 | Dav threshold =  1.00e-10\n",
            "Time elapsed =      1.415 | E =      -3.2667431000 | DE = 0.00e+00 | DW = 3.66e-20\n",
            "\n",
            "Sweep =    8 | Direction =  forward | Bond dimension =  200 | Noise =  0.00e+00 | Dav threshold =  1.00e-09\n",
            "Time elapsed =      1.526 | E =      -3.2667431000 | DE = -1.78e-15 | DW = 5.13e-20\n",
            "\n",
            "Ground state energy =   -3.266743099950349\n",
            "\n",
            "Sweep =    0 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.022 | F = (0.6266622731,0.0000000000) | DW = 7.22e-25\n",
            "\n",
            "Sweep =    1 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.051 | F = (0.7050283557,0.0000000000) | DF = (7.84e-02,0.00e+00) | DW = 9.91e-25\n",
            "\n",
            "Sweep =    2 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.076 | F = (0.7050283557,0.0000000000) | DF = (4.44e-16,0.00e+00) | DW = 7.16e-25\n",
            "\n",
            "Sweep =    3 | Direction =  forward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.112 | F = (0.7050283557,0.0000000000) | DF = (-1.11e-16,0.00e+00) | DW = 1.77e-24\n",
            "\n",
            "Sweep =    4 | Direction = backward | BRA bond dimension =  200 | Noise =  0.00e+00\n",
            "Time elapsed =      0.148 | F = (0.7050283557,0.0000000000) | DF = (-1.11e-16,0.00e+00) | DW = 7.19e-25\n",
            "\n",
            "it =     0 ( 0.0 %)\n",
            "it =    25 ( 1.0 %)\n",
            "it =    50 ( 2.0 %)\n",
            "it =    75 ( 3.0 %)\n",
            "it =   100 ( 4.0 %)\n",
            "it =   125 ( 5.0 %)\n",
            "it =   150 ( 6.0 %)\n",
            "it =   175 ( 7.0 %)\n",
            "it =   200 ( 8.0 %)\n",
            "it =   225 ( 9.0 %)\n",
            "it =   250 (10.0 %)\n",
            "it =   275 (11.0 %)\n",
            "it =   300 (12.0 %)\n",
            "it =   325 (13.0 %)\n",
            "it =   350 (14.0 %)\n",
            "it =   375 (15.0 %)\n",
            "it =   400 (16.0 %)\n",
            "it =   425 (17.0 %)\n",
            "it =   450 (18.0 %)\n",
            "it =   475 (19.0 %)\n",
            "it =   500 (20.0 %)\n",
            "it =   525 (21.0 %)\n",
            "it =   550 (22.0 %)\n",
            "it =   575 (23.0 %)\n",
            "it =   600 (24.0 %)\n",
            "it =   625 (25.0 %)\n",
            "it =   650 (26.0 %)\n",
            "it =   675 (27.0 %)\n",
            "it =   700 (28.0 %)\n",
            "it =   725 (29.0 %)\n",
            "it =   750 (30.0 %)\n",
            "it =   775 (31.0 %)\n",
            "it =   800 (32.0 %)\n",
            "it =   825 (33.0 %)\n",
            "it =   850 (34.0 %)\n",
            "it =   875 (35.0 %)\n",
            "it =   900 (36.0 %)\n",
            "it =   925 (37.0 %)\n",
            "it =   950 (38.0 %)\n",
            "it =   975 (39.0 %)\n",
            "it =  1000 (40.0 %)\n",
            "it =  1025 (41.0 %)\n",
            "it =  1050 (42.0 %)\n",
            "it =  1075 (43.0 %)\n",
            "it =  1100 (44.0 %)\n",
            "it =  1125 (45.0 %)\n",
            "it =  1150 (46.0 %)\n",
            "it =  1175 (47.0 %)\n",
            "it =  1200 (48.0 %)\n",
            "it =  1225 (49.0 %)\n",
            "it =  1250 (50.0 %)\n",
            "it =  1275 (51.0 %)\n",
            "it =  1300 (52.0 %)\n",
            "it =  1325 (53.0 %)\n",
            "it =  1350 (54.0 %)\n",
            "it =  1375 (55.0 %)\n",
            "it =  1400 (56.0 %)\n",
            "it =  1425 (57.0 %)\n",
            "it =  1450 (58.0 %)\n",
            "it =  1475 (59.0 %)\n",
            "it =  1500 (60.0 %)\n",
            "it =  1525 (61.0 %)\n",
            "it =  1550 (62.0 %)\n",
            "it =  1575 (63.0 %)\n",
            "it =  1600 (64.0 %)\n",
            "it =  1625 (65.0 %)\n",
            "it =  1650 (66.0 %)\n",
            "it =  1675 (67.0 %)\n",
            "it =  1700 (68.0 %)\n",
            "it =  1725 (69.0 %)\n",
            "it =  1750 (70.0 %)\n",
            "it =  1775 (71.0 %)\n",
            "it =  1800 (72.0 %)\n",
            "it =  1825 (73.0 %)\n",
            "it =  1850 (74.0 %)\n",
            "it =  1875 (75.0 %)\n",
            "it =  1900 (76.0 %)\n",
            "it =  1925 (77.0 %)\n",
            "it =  1950 (78.0 %)\n",
            "it =  1975 (79.0 %)\n",
            "it =  2000 (80.0 %)\n",
            "it =  2025 (81.0 %)\n",
            "it =  2050 (82.0 %)\n",
            "it =  2075 (83.0 %)\n",
            "it =  2100 (84.0 %)\n",
            "it =  2125 (85.0 %)\n",
            "it =  2150 (86.0 %)\n",
            "it =  2175 (87.0 %)\n",
            "it =  2200 (88.0 %)\n",
            "it =  2225 (89.0 %)\n",
            "it =  2250 (90.0 %)\n",
            "it =  2275 (91.0 %)\n",
            "it =  2300 (92.0 %)\n",
            "it =  2325 (93.0 %)\n",
            "it =  2350 (94.0 %)\n",
            "it =  2375 (95.0 %)\n",
            "it =  2400 (96.0 %)\n",
            "it =  2425 (97.0 %)\n",
            "it =  2450 (98.0 %)\n",
            "it =  2475 (99.0 %)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}