.. _sphx_glr_dimer_lattice_plot_energy.py:


Internal Energy in dimer solutions
==================================

Within the coexistence region calculate for various temperatures the
internal energy of each solution. In the IPT approximation the
insulator always presents itself as the lowest internal energy
solution.



.. image:: /dimer_lattice/images/sphx_glr_plot_energy_001.png
    :align: center





.. 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
    from dmft import dimer


    def loop_urange(urange, tp, beta):
        ekin, epot = [], []
        tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**10))
        giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)

        for u_int in urange:
            giw_d, giw_o, _ = dimer.ipt_dmft_loop(
                beta, u_int, tp, giw_d, giw_o, tau, w_n, 1e-4)

            ekin.append(dimer.ekin(giw_d, giw_o, w_n, tp, beta))
            epot.append(dimer.epot(giw_d, w_n, beta,
                                   u_int ** 2 / 4 + tp**2 + 0.25, ekin[-1], u_int))

        return np.array(ekin), np.array(epot)


    def plot_energy(beta, tp, urange, ax):
        met = loop_urange(urange, tp, beta)
        ins = loop_urange(urange[::-1], tp, beta)
        ax.plot(urange, np.sum(met, 0))
        ax.plot(urange, np.sum(ins, 0)[::-1])
        ax.set_ylabel(r'$\beta={}$'.format(beta))


    fig, ax = plt.subplots(3, 1, sharex=True, sharey=True)

    URANGE = np.linspace(2, 3.5, 30)
    plot_energy(40., 0.3, URANGE, ax[0])
    plot_energy(80., 0.3, URANGE, ax[1])
    plot_energy(200., 0.3, URANGE, ax[2])
    plt.savefig('IPT_HinU_tp0.3.pdf')
    plt.xlabel(r"$U/D$")
    plt.show()

**Total running time of the script:** ( 0 minutes  9.512 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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