.. _sphx_glr_auto_examples_twosite_plot_halffill_matsubara.py:


================================================
Following the Metal to Mott insulator Transition
================================================

Sequence of plots showing the transfer of spectral weight for a Hubbard
Model in the Bethe Lattice as the local interaction is raised.




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


    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_matsubara_001.png
            :scale: 47

    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_matsubara_002.png
            :scale: 47

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      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_matsubara_003.png
            :scale: 47

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      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_matsubara_004.png
            :scale: 47





.. code-block:: python


    # Code source: Óscar Nájera
    # License: BSD 3 clause
    from __future__ import division, absolute_import, print_function
    import matplotlib.pyplot as plt
    import numpy as np
    from dmft.twosite import refine_mat_solution

    axis = 'matsubara'
    du = 0.05
    beta = 50
    u_int = [2., 4.5, 5.85, 6.]

    out_file = axis+'_halffill_b{}_dU{}'.format(beta, du)
    res = np.load(out_file+'.npy')

    for u in u_int:
        ind = np.abs(res[:, 0] - u).argmin()

        f, (ax1, ax2) = plt.subplots(2, sharex=True)
        ax1.set_title('Transition to Mott Insulator at '
                      '$\\beta=${} and U/D={}'.format(beta, u/2))

        sim = refine_mat_solution(res[ind, 2], u)

        w = sim.omega.imag
        s = sim.GF[r'$\Sigma$']
        g = sim.GF['Imp G']

        ax1.plot(w, g.imag, 'b+')
        ax1.set_xlim([w.min(), w.max()])

        ax2.plot(w, s.imag, 'b+')
        bound = s.imag.min() * 1.2
        ax2.set_ylim([np.max([bound, -25]), 0])

        ax1.set_ylabel(r'$\Im m G_{imp}(\omega)$', color='b')
        ax2.set_ylabel(r'$\Im m \Sigma(\omega)$', color='b')
        ax2.set_xlabel('$i\\omega_n / t$')

**Total running time of the script:** ( 0 minutes  0.745 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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