.. _sphx_glr_auto_examples_twosite_plot_halffill.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_001.png
            :scale: 47

    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_002.png
            :scale: 47

    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_003.png
            :scale: 47

    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_004.png
            :scale: 47

    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_halffill_005.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 slaveparticles.quantum import dos

    axis = 'real'
    du = 0.05
    beta = 1e3
    u_int = [0.5, 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.where(np.abs(res[:, 0] - u) < 1e-3)[0][0]

        f, (ax1, ax2, ax3) = plt.subplots(3, sharex=True)
        ax1.set_title('Transition to Mott Insulator at '
                      '$\\beta=${} and U/D={}'.format(beta, u/2))
        f.subplots_adjust(hspace=0)

        w = res[ind, 2].omega
        s = res[ind, 2].GF[r'$\Sigma$']
        g = res[ind, 2].GF['Imp G']
        ra = w+u/2.-s
        rho = dos.bethe_lattice(ra, res[ind, 2].t)

        ax1.plot(w, rho)
        ax1.set_xlim([-6, 6])
        ax1.set_ylim([0, 0.36])

        ax2.plot(w, s)
        ax2.set_ylim([-6, 9])

        ax3.plot(w, g)
        ax3.set_ylim([-6, 6])

        ax1.set_ylabel(r'$A(\omega)$')
        ax2.set_ylabel(r'$\Sigma(\omega)$')
        ax3.set_ylabel(r'$G_{imp}(\omega)$')
        ax3.set_xlabel('$\\omega / t$')

**Total running time of the script:** ( 0 minutes  1.221 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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