.. _sphx_glr_auto_examples_IPT_plot_bandwidth_transition.py:


========================
IPT bandwidth controlled
========================

Have a look at the coexistence region and the metal insulator
transition from the point of view of a change in bandwidth




.. code-block:: python


    from __future__ import division, absolute_import, print_function

    from dmft.ipt_imag import dmft_loop
    from dmft.common import greenF, tau_wn_setup, fit_gf
    from dmft.twosite import matsubara_Z

    import numpy as np
    import matplotlib.pylab as plt


    def hysteresis(beta, D_range):
        log_g_sig = []
        tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**11))
        g_iwn = greenF(w_n, D=1)
        for D in D_range:
            g_iwn, sigma = dmft_loop(1, D / 2, g_iwn, w_n, tau)
            log_g_sig.append((g_iwn, sigma))
        return log_g_sig


    results = []
    Drange = np.linspace(0.25, .75, 61)
    Drange = np.concatenate((Drange[::-1], Drange + .005))
    betarange = [16, 17.85, 19.2, 20., 21.3, 25, 50, 100, 200, 512]
    for beta in betarange:
        results.append(hysteresis(beta, Drange))








Quasiparticle weight
--------------------



.. code-block:: python


    figz, axz = plt.subplots()
    for beta, result in zip(betarange, results):
        u_zet = [matsubara_Z(sigma.imag, beta) for _, sigma in result]
        axz.plot(Drange, u_zet, '+-', label='$\\beta={}$'.format(beta))
        axz.set_title('Hysteresis loop of the quasiparticle weigth')
        axz.legend(loc=0)
        axz.set_ylabel('Z')
        axz.set_xlabel('D/U')





.. image:: /auto_examples/IPT/images/sphx_glr_plot_bandwidth_transition_001.png
    :align: center




Spectral density at Fermi level
-------------------------------



.. code-block:: python


    figf, axf = plt.subplots()
    for beta, result in zip(betarange, results):
        tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=3))
        u_fl = [-fit_gf(w_n, g_iwn.imag)(0.)for g_iwn, _ in result]
        axf.plot(Drange, u_fl, 'x:', label='$\\beta={}$'.format(beta))

    axf.set_ylabel('Dos(0)')
    axf.set_xlabel('D/U')




.. image:: /auto_examples/IPT/images/sphx_glr_plot_bandwidth_transition_002.png
    :align: center




Double occupation
-----------------




.. code-block:: python


    figd, axd = plt.subplots()
    for beta, result in zip(betarange, results):
        tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**11))
        V = np.asarray([2 * (0.5 * s * g + 1 / 8. / w_n**2).real.sum() / beta
                        for (g, s) in result]) - 0.25 * beta * 1 / 8.

        D = 2. * V + 0.25
        axd.plot(Drange, D, '-', label='$\\beta={}$'.format(beta))

    axd.set_title('Double occupation')
    axd.legend(loc=0)
    axd.set_ylabel(r'$\langle n_\uparrow n_\downarrow \rangle$')
    axd.set_xlabel('D/U')



.. image:: /auto_examples/IPT/images/sphx_glr_plot_bandwidth_transition_003.png
    :align: center




**Total running time of the script:** ( 0 minutes  31.853 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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