.. _sphx_glr_dimer_lattice_plot_build_dispersions.py:


=====================================================
Various schemes for obtaining the spectral dispersion
=====================================================





.. rst-class:: sphx-glr-horizontal


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.. code-block:: python

    # Created Mon Apr 11 14:17:29 2016
    # Author: Óscar Nájera

    from __future__ import division, absolute_import, print_function

    import matplotlib.pyplot as plt
    import numpy as np

    import dmft.common as gf
    import dmft.dimer as dimer
    import dmft.ipt_imag as ipt
    from dmft.plot import plot_band_dispersion


    def ipt_u_tp(u_int, tp, beta, seed='ins'):
        tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=1024))
        giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
        if seed == 'ins':
            giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j

        giw_d, giw_o, loops = dimer.ipt_dmft_loop(
            beta, u_int, tp, giw_d, giw_o, tau, w_n, 1e-12)
        g0iw_d, g0iw_o = dimer.self_consistency(
            1j * w_n, 1j * giw_d.imag, giw_o.real, 0., tp, 0.25)
        siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)

        return siw_d, siw_o, w_n


    def construct_dispersions(BETA, u_int, tp, seed):
        siw_d, siw_o, w_n = ipt_u_tp(u_int, tp, BETA, seed)

        w = np.linspace(-3, 3, 800)
        eps_k = np.linspace(-1., 1., 61)
        w_set = np.arange(200)

        ss = gf.pade_continuation(
            1j * siw_d.imag + siw_o.real, w_n, w, w_set)  # A-bond
        sa = gf.pade_continuation(
            1j * siw_d.imag - siw_o.real, w_n, w, w_set)  # bond
        lat_gfs = 1 / np.add.outer(-eps_k, w - tp + 5e-2j - ss)
        lat_gfa = 1 / np.add.outer(-eps_k, w + tp + 5e-2j - sa)
        Aw = np.clip(-.5 * (lat_gfa + lat_gfs).imag / np.pi, 0, 2)

        title = 'Spectral Function dispersion\n$U={}$, $t_\\perp={}$, $\\beta={}$'.format(
            u_int, tp, BETA)

        # Continuate in Sigma Diagonal then return to local
        plot_band_dispersion(w, Aw, 'Local ' + title, eps_k, 'intensity')
        file_r = "Aew_B{}U{}tp{}_{}_".format(BETA, u_int, tp, seed)
        plt.savefig(file_r + 'psl.png', format='png',
                    transparent=False, bbox_inches='tight', pad_inches=0.05)

        # Continuate in Sigma Diagonal only plot anti-bonding
        Aw = np.clip(-lat_gfs.imag / np.pi, 0, 2)
        plot_band_dispersion(w,  Aw, 'Anti-Bond ' + title, eps_k,  'intensity')
        plt.savefig(file_r + 'psa.png', format='png',
                    transparent=False, bbox_inches='tight', pad_inches=0.05)

        # Continuate the dispersion on G(e, w)_AA
        Ag = []
        for e in eps_k:
            gd = dimer.mat_inv(1j * w_n - e - 1j * siw_d.imag, -tp - siw_o.real)[0]
            Ag.append(np.clip(
                np.abs(-gf.pade_continuation(gd, w_n, w + 1e-2j, w_set).imag / np.pi), 0, 2))

        plot_band_dispersion(w, np.asarray(
            Ag), 'Local ' + title, eps_k, 'intensity')
        plt.savefig(file_r + 'pgl.png', format='png',
                    transparent=False, bbox_inches='tight', pad_inches=0.05)

        # Continuate on G(e, w)_AA but skipping frequencies for smooth output
        w_set = np.arange(0, 200, 4)
        Ag = []
        for e in eps_k:
            gd = dimer.mat_inv(1j * w_n - e - 1j * siw_d.imag, -tp - siw_o.real)[0]
            Ag.append(np.clip(
                np.abs(-gf.pade_continuation(gd, w_n, w + 1e-2j, w_set).imag / np.pi), 0, 2))

        plot_band_dispersion(w, np.asarray(
            Ag), 'Local ' + title, eps_k, 'intensity')
        plt.savefig(file_r + 'pgls.png', format='png',
                    transparent=False, bbox_inches='tight', pad_inches=0.05)


    construct_dispersions(100., 2.5, .3, 'met')
    construct_dispersions(100., 2.5, .3, 'ins')

**Total running time of the script:** ( 0 minutes  7.588 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_build_dispersions.py <plot_build_dispersions.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_build_dispersions.ipynb <plot_build_dispersions.ipynb>`

.. rst-class:: sphx-glr-signature

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