.. _sphx_glr_dimer_lattice_plot_line_dispersion.py: =================================== Dispersion of the spectral function =================================== .. code-block:: python # Author: Óscar Nájera from __future__ import (absolute_import, division, print_function, unicode_literals) import matplotlib.pyplot as plt import numpy as np import dmft.common as gf import dmft.dimer as dimer import dmft.ipt_imag as ipt from dmft.plot import plot_band_dispersion def loop_u_tp(u_range, tprange, beta, seed='mott gap'): tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=max(5 * beta, 256))) giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.) if seed == 'mott gap': giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j giw_s = [] sigma_iw = [] iterations = [] for u_int, tp in zip(u_range, tprange): giw_d, giw_o, loops = dimer.ipt_dmft_loop( beta, u_int, tp, giw_d, giw_o, tau, w_n) giw_s.append((giw_d, giw_o)) iterations.append(loops) g0iw_d, g0iw_o = dimer.self_consistency( 1j * w_n, 1j * giw_d.imag, giw_o.real, 0., tp, 0.25) siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n) sigma_iw.append((siw_d.copy(), siw_o.copy())) print(np.array(iterations)) return np.array(giw_s), np.array(sigma_iw), w_n def plot_greenfunct(w, gfunc, title, ylabel, ax=None): if ax is None: f, ax = plt.subplots(1) ax.plot(w, gfunc.real, label=r'$\Re e$' + ylabel) ax.plot(w, -gfunc.imag, label=r'$-\Im m$' + ylabel) ax.legend(loc=0) ax.set_xlabel(r'$\omega$') ax.set_ylabel(ylabel + r'$(\omega)$') ax.set_title(title) ax.set_ylim([-3, 3]) return ax def plot_pole_eq(w, gf, sig, title): plt.figure() plt.plot(w, sig.imag, label=r'$\Im m \Sigma$') plt.plot(w, (1 / gf).real, label=r'$\Re e G^{-1}$') plt.plot(w, -gf.imag, label='DOS') plt.legend(loc=0) plt.title(title) plt.ylim([-3, 3]) def plot_dispersions(giw_s, sigma_iw, ur, tp, w_n, w, w_set): for U, (giw_d, giw_o), (sig_d, sig_o) in zip(ur, giw_s, sigma_iw): gs, ga = dimer.pade_diag(giw_d, giw_o, w_n, w_set, w) ss, sa = dimer.pade_diag(sig_d, sig_o, w_n, w_set, w) gst = gf.semi_circle_hiltrans( w - tp - (ss.real - 1j * np.abs(ss.imag))) lat_gfs = 1 / np.add.outer(-eps_k, w - tp + 5e-3j - ss) lat_gfa = 1 / np.add.outer(-eps_k, w + tp + 5e-3j - sa) #Aw = np.clip(-.5 * (lat_gfa + lat_gfs).imag / np.pi, 0, 2) Aw = np.clip(-lat_gfs.imag / np.pi, 0, 2) title = r'IPT lattice dimer $U={}$, $t_\perp={}$, $\beta={}$'.format( U, tp, BETA) ax = plot_greenfunct(w, gs, title, r'$G$') plot_greenfunct(w, gst, title, r'$G$', ax) plot_greenfunct(w, 1 / (w - tp - .25 * gst), title, r'$G0$', ax) ax = plot_greenfunct(w, ss, title, r'$\Sigma$') plot_pole_eq(w, gst, ss, title) plot_band_dispersion(w, Aw, title, eps_k) Metals ------ .. code-block:: python urange = [1.5, 2., 2.175, 2.5, 3.] BETA = 100. tp = 0.3 giw_s, sigma_iw, w_n = loop_u_tp(urange, tp * np.ones_like(urange), BETA, "M") w = np.linspace(-4, 4, 800) eps_k = np.linspace(-1., 1., 61) w_set = np.concatenate((np.arange(100), np.arange(100, 200, 2))) plot_dispersions(giw_s, sigma_iw, urange, tp, w_n, w, w_set) .. rst-class:: sphx-glr-horizontal * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_001.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_002.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_003.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_004.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_005.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_006.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_007.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_008.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_009.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_010.png :scale: 47 * .. image:: 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image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_023.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_024.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_025.png :scale: 47 .. rst-class:: sphx-glr-script-out Out:: [171 109 94 75 42] Insulators ---------- .. code-block:: python tp = 0.3 urange = [0, .5, 1, 2.175, 2.5, 3., 3.5, 4., 5.] giw_s, sigma_iw, w_n = loop_u_tp( urange, tp * np.ones_like(urange), BETA) eps_k = np.linspace(-1., 1., 61) plot_dispersions(giw_s, sigma_iw, urange, tp, w_n, w, w_set) .. rst-class:: sphx-glr-horizontal * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_026.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_027.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_028.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_029.png :scale: 47 * .. image:: 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:scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_066.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_067.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_068.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_069.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_070.png :scale: 47 .. rst-class:: sphx-glr-script-out Out:: [308 197 178 102 75 42 18 10 8] Insulators ---------- .. code-block:: python tp = 0.5 urange = [0, .5, 2.175, 2.5, 3., 3.5, 4., 5.] giw_s, sigma_iw, w_n = loop_u_tp( urange, tp * np.ones_like(urange), BETA) eps_k = np.linspace(-1., 1., 61) plot_dispersions(giw_s, sigma_iw, urange, tp, w_n, w, w_set) .. rst-class:: sphx-glr-horizontal * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_071.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_072.png :scale: 47 * .. image:: 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:scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_109.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_110.png :scale: 47 .. rst-class:: sphx-glr-script-out Out:: [275 191 70 17 11 10 9 8] Insulators ---------- .. code-block:: python tp = 0.8 urange = [0, .5, 1.2, 1.5, 2., 2.5, 3., 3.5, 4., 5.] giw_s, sigma_iw, w_n = loop_u_tp( urange, tp * np.ones_like(urange), BETA) eps_k = np.linspace(-1., 1., 61) plot_dispersions(giw_s, sigma_iw, urange, tp, w_n, w, w_set) .. rst-class:: sphx-glr-horizontal * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_111.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_112.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_113.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_114.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_115.png :scale: 47 * .. image:: 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:scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_152.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_153.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_154.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_155.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_156.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_157.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_158.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_159.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_160.png :scale: 47 .. rst-class:: sphx-glr-script-out Out:: [185 136 48 25 14 10 9 8 7 7] Insulators ---------- .. code-block:: python tp = 0.95 urange = [0, .5, 1.2, 1.5, 2., 2.5, 3., 3.5, 4., 5.] giw_s, sigma_iw, w_n = loop_u_tp( urange, tp * np.ones_like(urange), BETA) eps_k = np.linspace(-1., 1., 61) plot_dispersions(giw_s, sigma_iw, urange, tp, w_n, w, w_set) #urange = [3.2] #beta = 100. #tp = 0.2 # giw_s, sigma_iw, w_n = loop_u_tp( # urange, tp * np.ones_like(urange), beta) # #w = np.linspace(-8, 8, 1600) #w_set = np.concatenate((np.arange(80), np.arange(90, 140, 25))) #eps_k = np.linspace(-2., 1., 61) #ss, gs = plot_dispersions(giw_s, sigma_iw, urange, tp, w_n, w, w_set) # # #tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=max(5 * beta, 256))) #tp = 0.2 # g0iw_d, g0iw_o = dimer.self_consistency( # 1j * w_n, giw_s[0], giw_s[0], 0., tp, 0.25) #siw_d, siw_o = ipt.dimer_sigma(urange[0], tp, g0iw_d, g0iw_o, tau, w_n) #giw_d, giw_o = dimer.dimer_dyson(g0iw_d, g0iw_o, siw_d, siw_o) # g0iw_d, g0iw_o = dimer.self_consistency( # 1j * w_n, giw_s[0], giw_s[0], 0., tp, 0.25) #siw_d, siw_o = ipt.dimer_sigma(urange[0], tp, g0iw_d, g0iw_o, tau, w_n) # ss, gs = plot_dispersions( # np.array([giw_d, giw_o]), np.array([siw_d, siw_o]), urange, tp, w_n, w, # w_set) .. rst-class:: sphx-glr-horizontal * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_161.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_162.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_163.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_164.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_165.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_166.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_167.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_168.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_169.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_170.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_171.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_172.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_173.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_174.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_175.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_176.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_177.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_178.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_179.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_180.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_181.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_182.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_183.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_184.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_185.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_186.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_187.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_188.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_189.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_190.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_191.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_192.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_193.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_194.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_195.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_196.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_197.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_198.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_199.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_200.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_201.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_202.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_203.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_204.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_205.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_206.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_207.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_208.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_209.png :scale: 47 * .. image:: /dimer_lattice/images/sphx_glr_plot_line_dispersion_210.png :scale: 47 .. rst-class:: sphx-glr-script-out Out:: [95 62 21 16 12 10 8 7 7 6] **Total running time of the script:** ( 0 minutes 29.589 seconds) .. container:: sphx-glr-footer .. container:: sphx-glr-download :download:`Download Python source code: plot_line_dispersion.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_line_dispersion.ipynb ` .. rst-class:: sphx-glr-signature `Generated by Sphinx-Gallery `_