.. _sphx_glr_auto_examples_twosite_plot_dispersion.py:


Spectral dispersion of insulator
================================

What does the insulator show for Hubbard bands. They are sharp as in
the Hubbard I approximation.





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


    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_dispersion_001.png
            :scale: 47

    *

      .. image:: /auto_examples/twosite/images/sphx_glr_plot_dispersion_002.png
            :scale: 47


.. rst-class:: sphx-glr-script-out

 Out::

    4 9.2695705889e-06 [ 0.5  0.5]




|


.. code-block:: python

    # Author: 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 TwoSite_Real
    from slaveparticles.quantum import dos
    import dmft.common as gf

    fig = plt.figure()

    solver = TwoSite_Real
    U = 4
    beta = 1e5
    sim = solver(beta, 0.5)
    sim.mu = U / 2
    convergence = False
    hyb = 0.4
    while not convergence:
        old = hyb
        sim.solve(U / 2, U, old)
        hyb = sim.hyb_V()
        hyb = (hyb + old) / 2
        convergence = np.abs(old - hyb) < 1e-5

    print(U, hyb, sim.ocupations())
    sim.solve(U / 2, U, hyb)
    hyb = sim.hyb_V()

    plt.plot(sim.omega, sim.GF[r'$\Sigma$'])
    plt.plot(sim.omega, sim.GF[r'Imp G'])

    w = sim.omega
    s = sim.GF[r'$\Sigma$']
    g = sim.GF['Imp G']
    ra = w + sim.mu - s
    rho = dos.bethe_lattice(ra, sim.t)
    plt.plot(w, rho)
    g = gf.semi_circle_hiltrans(ra + 0.01j)
    plt.plot(w, g.imag)

    plt.figure()
    eps_k = np.linspace(-1., 1., 61)
    lat_gfs = 1 / np.add.outer(-eps_k, ra + 0.01j)
    Aw = np.clip(-lat_gfs.imag / np.pi, 0, 2,)
    x, y = np.meshgrid(eps_k, w)
    plt.pcolormesh(x, y, Aw.T, cmap=plt.get_cmap(r'viridis'), vmin=0, vmax=2)

**Total running time of the script:** ( 0 minutes  0.292 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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