.. _sphx_glr_auto_examples_plot_bethe.py:


Bethe lattice semi-elliptical DOS
=================================

The Bethe lattice has a simple form of the self-consistency. This is
solved by iteration where introducing the poles in the Green function
to recover such density of states.




.. image:: /auto_examples/images/sphx_glr_plot_bethe_001.png
    :align: center





.. code-block:: python


    import numpy as np
    import matplotlib.pyplot as plt

    omega = 1e-3j + np.linspace(-4, 4, 800)
    gf_w = np.zeros_like(omega)
    t = 0.5

    for i in range(1, int(1e4 + 1)):
        gf_w = 1 / (omega - t**2 * gf_w)
        if i in [1, 4, 10000]:
            plt.plot(omega.real, gf_w.real, label='iteration ' + str(i))

    plt.plot(omega.real, -gf_w.imag / np.pi, label=r'$A(\omega)$')
    plt.legend(loc=0)
    plt.ylim([-3, 3])
    plt.xlabel(r'$\omega$')
    plt.ylabel(r'$\Re e G(\omega)$')

**Total running time of the script:** ( 0 minutes  0.402 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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