.. _sphx_glr_dimer_lattice_plot_integrated_spectra.py:


===================================
Dispersion of the spectral function
===================================

Comparison of the energy resolved spectral functions in the Dimer Hubbard
Model in the coexistence region. For the metallic and insulating
solution. Figure is discussed in reference [Najera2017]_


.. [Najera2017] O. Nájera, Civelli, M., V. Dobrosavljevic, & Rozenberg,
  M. J. (2017). Resolving the VO_2 controversy: Mott mechanism dominates
  the insulator-to-metal transition. Physical Review B, 95(3),
  035113. http://dx.doi.org/10.1103/physrevb.95.035113





.. image:: /dimer_lattice/images/sphx_glr_plot_integrated_spectra_001.png
    :align: center





.. code-block:: python

    # Author: Óscar Nájera

    from __future__ import (absolute_import, division, print_function,
                            unicode_literals)

    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=2**12))
        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 calculate_Aw(sig_d, sig_o, w_n, w_set, w, eps_k, tp):
        ss, sa = dimer.pade_diag(1j * sig_d.imag, sig_o.real, w_n, w_set, w)

        lat_gfs = 1 / np.add.outer(-eps_k, w - tp + 7e-3j - ss)
        lat_gfa = 1 / np.add.outer(-eps_k, w + tp + 7e-3j - sa)
        Aw = -.5 * (lat_gfa + lat_gfs).imag / np.pi

        return Aw, ss, sa


    def plot_spectra(u_int, tp, beta, w, w_set, eps_k, axes):
        pdm, pam, pdi, pai = axes
        x, y = np.meshgrid(eps_k, w)
        # metal
        siw_d, siw_o, w_n = ipt_u_tp(u_int, tp, beta, 'met')
        Aw, ss, sa = calculate_Aw(siw_d, siw_o, w_n, w_set, w, eps_k, tp)
        Aw = np.clip(Aw, 0, 1,)
        pdm.pcolormesh(x, y, Aw.T, cmap=plt.get_cmap(r'inferno'))
        gsts = gf.semi_circle_hiltrans(w - tp - (ss.real - 1j * np.abs(ss.imag)))
        gsta = gf.semi_circle_hiltrans(w + tp - (sa.real - 1j * np.abs(sa.imag)))
        gloc = 0.5 * (gsts + gsta)
        pam.plot(-gloc.imag / np.pi, w)

        # insulator
        siw_d, siw_o, w_n = ipt_u_tp(u_int, tp, beta, 'ins')
        Aw, ss, sa = calculate_Aw(siw_d, siw_o, w_n, w_set, w, eps_k, tp)
        Aw = np.clip(Aw, 0, 1,)
        pdi.pcolormesh(x, y, Aw.T, cmap=plt.get_cmap(r'inferno'))
        gsts = gf.semi_circle_hiltrans(w - tp - (ss.real - 1j * np.abs(ss.imag)))
        gsta = gf.semi_circle_hiltrans(w + tp - (sa.real - 1j * np.abs(sa.imag)))
        gloc = 0.5 * (gsts + gsta)
        pai.plot(-gloc.imag / np.pi, w)


    def write_labels_e_struct(axes):
        axes[0].set_xticklabels([])
        axes[0].set_yticks(np.linspace(-2.5, 2.5, 5))
        axes[1].set_yticks(np.linspace(-2.5, 2.5, 5))
        axes[1].set_yticklabels([])
        axes[1].set_xticklabels([])
        axes[2].set_yticks(np.linspace(-2.5, 2.5, 5))
        axes[3].set_yticks(np.linspace(-2.5, 2.5, 5))
        axes[3].set_yticklabels([])
        axes[3].set_xticklabels([])
        axes[0].set_ylabel(r'$\omega$')
        axes[2].set_ylabel(r'$\omega$')
        axes[2].set_xlabel(r'$\epsilon$')
        axes[3].set_xlabel(r'$A(\omega)$')


    w = np.linspace(-3, 3, 1000)
    eps_k = np.linspace(-1., 1., 61)
    w_set = np.arange(150)
    for U in [2.5]:
        fig, ax = plt.subplots(2, 2, gridspec_kw=dict(
            wspace=0.05, hspace=0.1, width_ratios=[3, 1]))
        axes = ax.flatten()
        plot_spectra(U, .3, 100, w, w_set, eps_k, axes)

        write_labels_e_struct(axes)
        axes[0].set_title(
            r"$\beta={}$, $t_\perp={}$, $U={}$".format(100, .3, U))

    #plt.savefig('ipt_arpes_MIT.pdf', format='pdf', transparent=False, bbox_inches='tight', pad_inches=0.05)

**Total running time of the script:** ( 0 minutes  1.263 seconds)



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