.. _sphx_glr_dimer_lattice_nature_dimer_plot_dimer_transition.py:


Dimer Mott transition
=====================

Follow the spectral function from the correlated metal into the dimer
Mott insulator. The spectral functions is decomposed into the bonding
and anti-bonding contributions to make it explicit that is is a
phenomenon of the quasiparticles opening a band gap.

Using real frequencies solver

.. seealso::
    :ref:`sphx_glr_dimer_lattice_nature_dimer_plot_order_param_transition.py`



.. code-block:: python


    # author: Óscar Nájera

    from __future__ import division, absolute_import, print_function

    import numpy as np
    import matplotlib.pyplot as plt

    import dmft.common as gf
    import dmft.ipt_real as ipt

    w = np.linspace(-4, 4, 2**12)
    dw = w[1] - w[0]

    beta = 800.
    nfp = gf.fermi_dist(w, beta)






The :math:`t_\perp/D=0.3` scenario
==================================




.. code-block:: python


    tp = 0.3
    gss = gf.semi_circle_hiltrans(w + 5e-3j - tp)
    gsa = gf.semi_circle_hiltrans(w + 5e-3j + tp)
    urange = np.arange(0.2, 3.3, 0.3)
    urange = [0.2, 1., 2., 3., 3.47, 3.5]
    plt.close('all')
    for i, U in enumerate(urange):
        (gss, gsa), (ss, sa) = ipt.dimer_dmft(
            U, tp, nfp, w, dw, gss, gsa, conv=1e-4)
        shift = -2.1 * i
        plt.plot(w, shift + -gss.imag, 'C0', lw=0.5)
        plt.plot(w, shift + -gsa.imag, 'C1', lw=0.5)
        plt.plot(w, shift + -(gss + gsa).imag / 2, 'k', lw=2.5)
        plt.axhline(shift, color='k', lw=0.5)
        plt.text(-2.8, 1.45 + shift, r"$U/D={}$".format(U), size=16)
    plt.xlabel(r'$\omega$')
    plt.xlim([-3, 3])
    plt.ylim([shift, 2.1])
    plt.yticks([])
    # plt.savefig('dimer_transition_spectra.pdf')




.. image:: /dimer_lattice/nature_dimer/images/sphx_glr_plot_dimer_transition_001.png
    :align: center




The :math:`t_\perp/D=0.8` scenario
==================================




.. code-block:: python

    w = np.linspace(-8, 8, 2**14)
    dw = w[1] - w[0]
    nfp = gf.fermi_dist(w, beta)
    tp = 0.8
    gss = gf.semi_circle_hiltrans(w + 5e-3j - tp)
    gsa = gf.semi_circle_hiltrans(w + 5e-3j + tp)
    urange = np.linspace(0.2, 1.64, 6)
    urange = [0.5, 1., 1.352, 2.5]
    plt.close('all')
    for i, U in enumerate(urange):
        (gss, gsa), (ss, sa) = ipt.dimer_dmft(
            U, tp, nfp, w, dw, gss, gsa, conv=1e-4)
        shift = -2.1 * i
        plt.plot(w, shift + -gss.imag, 'C0', lw=0.5)
        plt.plot(w, shift + -gsa.imag, 'C1', lw=0.5)
        plt.plot(w, shift + -(gss + gsa).imag / 2, 'k', lw=2.5)
        plt.text(-2.8, 1.45 + shift, r"$U/D={}$".format(U), size=16)
    plt.xlabel(r'$\omega$')
    plt.xlim([-3, 3])
    plt.ylim([shift, 2.1])
    plt.yticks([])
    # plt.savefig('dimer_transition_spectra_tp0.8.pdf')



.. image:: /dimer_lattice/nature_dimer/images/sphx_glr_plot_dimer_transition_002.png
    :align: center


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

 Out::

    Failed to converge in less than 3000 iterations


**Total running time of the script:** ( 2 minutes  1.693 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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