.. _sphx_glr_dimer_lattice_plot_comparing_spectra.py:


============================
Comparing Spectral functions
============================




.. 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


    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-13)
        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 plot_pole_eq(w, gf, sig, pole, sty, ax):
        ax.plot(w, -np.abs(sig.imag),
                'r' + sty, label=r'$\Im m \Sigma$')
        ax.plot(w, sig.real,
                'g' + sty, label=r'$\Re e \Sigma$')
        ax.plot(w, -gf.imag / np.pi, 'b' + sty,  label='DOS')
        if pole:
            ax.plot(w, (1 / gf).real, 'c' + sty, label=r'$\Re e G^{-1}$')
        ax.set_ylim([-1, .7])
        ax.axvline(0)
        ax.axhline(0)
        ax.set_xticks(np.arange(-3, 4))
        ax.set_xticklabels(np.arange(-3, 4))
        ax.set_yticklabels([])


    def plot_spectral(u_int, tp, BETA, seed, w, w_set, pole, sty, ax):

        siw_d, siw_o, w_n = ipt_u_tp(u_int, tp, BETA, seed)
        ss, _ = dimer.pade_diag(siw_d, siw_o, w_n, w_set, w)
        gst = gf.semi_circle_hiltrans(w - tp - (ss.real - 1j * np.abs(ss.imag)))

        plot_pole_eq(w, gst, ss, pole, sty, ax)








Metals
------




.. code-block:: python

    BETA = 100.
    w = np.linspace(-4, 4, 800)
    w_set = np.concatenate((np.arange(75), np.arange(75, 150, 20)))
    f, ax = plt.subplots(2, 3, sharex=True)
    ax[0, 0].set_title(r'$U=2.5$')
    ax[0, 0].set_ylabel(r'$t_\perp=0$ $\Im m \Sigma (\omega)$  |   $A(\omega)$')
    plot_spectral(2.5, 0., BETA, 'met', w, w_set, True, '-', ax[0, 0])
    ax[0, 1].set_title(r'$U=2.9$')
    plot_spectral(2.9, 0., BETA, 'met', w, w_set, False, '-', ax[0, 1])
    plot_spectral(2.9, 0., BETA, 'ins', w, w_set, False, '-', ax[0, 1])
    ax[0, 2].set_title(r'$U=3.5$')
    plot_spectral(3.5, 0., BETA, 'ins', w, w_set, True, '-', ax[0, 2])

    ax[1, 0].set_ylabel(
        r'$t_\perp=0.3$ $\Im m \Sigma (\omega)$ |  $A(\omega)$    ')
    plot_spectral(2.5, 0.3, BETA, 'met', w, w_set, True, '-', ax[1, 0])
    plot_spectral(2.9, 0.3, BETA, 'met', w, w_set, False, '-', ax[1, 1])
    plot_spectral(2.9, 0.3, BETA, 'ins', w, w_set, False, '-', ax[1, 1])
    plot_spectral(3.5, 0.3, BETA, 'ins', w, w_set, True, '-', ax[1, 2])
    ax[1, 0].set_xlabel(r'$\omega$')
    ax[1, 1].set_xlabel(r'$\omega$')
    ax[1, 2].set_xlabel(r'$\omega$')
    plt.tight_layout()
    plt.subplots_adjust(wspace=0, hspace=0)

    f, ax = plt.subplots(2, 3, sharex=True)
    ax[0, 0].set_title(r'$U=1.0$')
    ax[0, 0].set_ylabel(
        r'$t_\perp=0.5$ $\Im m \Sigma (\omega)$ |  $A(\omega)$     ')
    plot_spectral(1.0, 0.5, BETA, 'met', w, w_set, True, '-', ax[0, 0])
    ax[0, 1].set_title(r'$U=2.1$')
    plot_spectral(2.1, 0.5, BETA, 'met', w, w_set, False, '-', ax[0, 1])
    plot_spectral(2.1, 0.5, BETA, 'ins', w, w_set, False, '-', ax[0, 1])
    ax[0, 2].set_title(r'$U=3.0$')
    plot_spectral(3.0, 0.5, BETA, 'ins', w, w_set, True, '-', ax[0, 2])

    ax[1, 0].set_ylabel(
        r'$t_\perp=0.8$ $\Im m \Sigma (\omega)$ |  $A(\omega)$     ')
    plot_spectral(1.0, 0.8, BETA, 'met', w, w_set, True, '-', ax[1, 0])
    plot_spectral(2.1, 0.8, BETA, 'ins', w, w_set, False, '-', ax[1, 1])
    plot_spectral(3.0, 0.8, BETA, 'ins', w, w_set, True, '-', ax[1, 2])
    ax[1, 0].set_xlabel(r'$\omega$')
    ax[1, 1].set_xlabel(r'$\omega$')
    ax[1, 2].set_xlabel(r'$\omega$')
    plt.tight_layout()
    plt.subplots_adjust(wspace=0, hspace=0)

    f, a = plt.subplots()
    g, b = plt.subplots()
    w = np.linspace(-4, 4, 800)
    w_set = np.concatenate((np.arange(75), np.arange(75, 150, 20)))
    plot_spectral(2.9, 0.3, 100., 'met', w, w_set, False, '-', a)
    plot_spectral(2.9, 0.3, 100., 'ins', w, w_set, False, '-', b)
    a.set_xlabel(r'$\omega$')
    a.legend()
    b.set_xlabel(r'$\omega$')
    b.legend()



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


    *

      .. image:: /dimer_lattice/images/sphx_glr_plot_comparing_spectra_001.png
            :scale: 47

    *

      .. image:: /dimer_lattice/images/sphx_glr_plot_comparing_spectra_002.png
            :scale: 47

    *

      .. image:: /dimer_lattice/images/sphx_glr_plot_comparing_spectra_003.png
            :scale: 47

    *

      .. image:: /dimer_lattice/images/sphx_glr_plot_comparing_spectra_004.png
            :scale: 47




**Total running time of the script:** ( 0 minutes  4.591 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

    `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_