def window_conv_depr():
nwf_vec = np.array([5, 10, 20, 40, 80, 160, 320])
diff_vec = np.zeros_like(nwf_vec, dtype=np.float)
for idx, nwf in enumerate(nwf_vec):
d = analytic_solution(beta=2.0, U=5.0, nw=1, nwf=nwf)
diff = np.max(np.abs(d.gamma_m.data - d.gamma_m_num.data))
diff_vec[idx] = diff
print('nwf, diff =', idx, nwf, diff)
print(diff_vec)
from triqs.plot.mpl_interface import oplot, oplotr, oploti, plt
x = 1. / nwf_vec
plt.figure(figsize=(3.25, 3))
plt.plot(x, diff_vec, 'o-', alpha=0.75)
plt.xlabel(r'$1/n_{w}$')
plt.ylabel(r'$\max|\Gamma_{ana} - \Gamma_{num}|$')
plt.ylim([0, diff_vec.max()])
plt.xlim([0, x.max()])
plt.tight_layout()
plt.savefig('figure_bse_hubbard_atom_convergence.pdf')
plt.show()
def plot_field(out):
plt.figure(figsize=(3.25 * 2, 8))
for p in out.data:
subp = [2, 1, 1]
ax = plt.subplot(*subp)
subp[-1] += 1
oplotr(p.G_tau['up'], 'b', alpha=0.25)
oplotr(p.G_tau['dn'], 'g', alpha=0.25)
ax.legend().set_visible(False)
subp = [2, 1, 2]
plt.subplot(*subp)
subp[-1] += 1
plt.title(r'$\chi \approx %2.2f$' % out.chi)
plt.plot(out.h_vec, out.m_vec, '-og', alpha=0.5)
plt.plot(out.h_vec, out.m_ref_vec, 'xb', alpha=0.5)
plt.plot(out.h_vec, -out.chi * out.h_vec, '-r', alpha=0.5)
plt.tight_layout()
plt.savefig('figure_static_field.pdf')
for idx, nwf in enumerate(nwf_vec):
d = analytic_hubbard_atom(beta=2.0,
U=5.0,
nw=1,
nwf=nwf,
nwf_gf=2 * nwf)
diff_vec[idx] = np.max(np.abs(d.gamma_m.data - d.gamma_m_num.data))
print('nwf, diff =', idx, nwf, diff_vec[idx])
# ------------------------------------------------------------------
# -- Plot
from triqs.plot.mpl_interface import oplot, oplotr, oploti, plt
x = 1. / nwf_vec
plt.figure(figsize=(3.25, 3))
plt.plot(x, diff_vec, 'o-', alpha=0.75)
plt.xlabel(r'$1/n_{w}$')
plt.ylabel(r'$\max|\Gamma_{ana} - \Gamma_{num}|$')
plt.ylim([0, diff_vec.max()])
plt.xlim([0, x.max()])
plt.tight_layout()
plt.savefig('figure_bse_hubbard_atom_convergence.pdf')
plt.show()
# -- Extrapolation to nwf -> oo
ps = ParameterCollections(objects=ps)
x, y = 1. / ps.nwf, ps.chi_G
sidx = np.argsort(x)
x, y = x[sidx], y[sidx]
p = np.polyfit(x, y, 1)
y0 = np.polyval(p, 0)
X = np.linspace(0, x.max())
Y = np.polyval(p, X)
subp = [1, 2, 1]
plt.subplot(*subp)
subp[-1] += 1
plt.plot(0, y0, 'rx')
plt.plot(0, 0.3479, 'r+')
plt.subplot(*subp)
subp[-1] += 1
plt.plot(X, Y, '--k', lw=1.0, zorder=-100)
plt.plot(0, 0.3479, 'r+', label=r'Field')
plt.plot(0, y0, 'rx', label=r'BSE')
plt.grid(True)
plt.legend(loc='best', fontsize=8)
plt.xlabel(r'$1/N_\nu$')
plt.ylabel(r'$\chi(\mathbf{0})$')
plt.title(
r'$\lim_{n_\nu \rightarrow \infty} \, \chi(\mathbf{0}) \approx $' + \
'${:3.4f}$'.format(y0))
plt.tight_layout()
plt.savefig('figure_bse.svg')
plt.show()
from triqs.plot.mpl_interface import oplot, oplotr, plt
with HDFArchive('data_g2.h5', 'r') as a:
p = a['p']
plt.figure(figsize=(3.25 * 2.2, 2))
subp = [1, 3, 1]
opt = dict(cmap=plt.get_cmap('terrain_r'), vmin=0.0, vmax=0.01)
plt.subplot(*subp)
subp[-1] += 1
plt.title(r'$\chi^{(0)}_m$')
plt.imshow(np.squeeze(p.chi0_m.data).real, **opt)
plt.colorbar()
plt.subplot(*subp)
subp[-1] += 1
plt.title(r'$\chi_m$')
plt.imshow(np.squeeze(p.chi_m.data).real, **opt)
plt.colorbar()
plt.subplot(*subp)
subp[-1] += 1
plt.title(r'$\Gamma_m - U$')
plt.imshow((np.squeeze(p.gamma_m.data) - p.U).real,
cmap=plt.get_cmap('RdBu_r'),
vmin=-5,
vmax=5)
plt.colorbar()
plt.tight_layout()
plt.savefig('figure_g2.svg')
plt.show()
styles = {256: '^b', 128: '>r', 64: '<g', 32: '.m', 16: '.c', 8: '.y'}
for filename in filenames:
print('--> Loading:', filename)
with HDFArchive(filename, 'r') as s:
p = s['p']
if hasattr(p, 'chi'):
style = styles[p.nwf]
plt.plot(1. / p.beta, p.chi, style, alpha=0.5)
for nw in np.sort(list(styles.keys())):
style = styles[nw]
plt.plot([], [],
style,
alpha=0.5,
label=r'Analytic Tr$[\chi_m]/\beta^2$, $n_w=%i$' % nw)
# ------------------------------------------------------------------
plt.legend(loc='best', fontsize=6, frameon=False)
#plt.xlabel(r'$\beta$')
plt.xlabel(r'$T$')
plt.ylabel(r'$\chi_m$')
plt.loglog([], [])
plt.tight_layout()
plt.savefig('figure_hubbard_atom_static_magnetic_susceptibility.pdf')
plt.show()
ps = []
filenames = np.sort(glob.glob('data_B_*.h5'))
for filename in filenames:
with HDFArchive(filename, 'r') as a:
p = a['ps'].objects[-1]
ps.append(p)
ps = ParameterCollections(ps)
B, M = ps.B, ps.M
B = np.concatenate((-B[1:][::-1], B))
M = np.concatenate((-M[1:][::-1], M))
p = np.polyfit(M, B, 5)
m = np.linspace(-0.5, 0.5, num=1000)
b = np.polyval(p, m)
chi = 1. / np.polyval(np.polyder(p, 1), 0.).real
plt.figure(figsize=(3.25 * 1.5, 2.5 * 1.5))
plt.title(r'$\chi = \frac{dM}{dB}|_{B=0} \approx $' + '$ {:3.4f}$'.format(chi))
plt.plot(B, M, 'o', alpha=0.75, label='DMFT field')
plt.plot(b, m, '-', alpha=0.75, label='Poly fit')
plt.legend(loc='upper left')
plt.grid(True)
plt.xlabel(r'$B$')
plt.ylabel(r'$M$')
plt.xlim([B.min(), B.max()])
plt.ylim([-0.5, 0.5])
plt.tight_layout()
plt.savefig('figure_field.svg')
plt.show()
vmax = np.max(data.real)
plt.title('Square-lattice ' + r'$\chi_0(q, \omega=0)$, $\beta=%2.2f$' % beta)
plt.pcolor(qx.reshape((n_k, n_k)),
qy.reshape((n_k, n_k)),
data.reshape((n_k, n_k)).real,
cmap='magma',
vmin=0,
vmax=vmax)
plt.colorbar()
plt.axis('equal')
plt.xlabel('$q_x/\pi$')
plt.ylabel('$q_y/\pi$')
plt.tight_layout()
plt.savefig('figure_chi0q_w0_square_latt.pdf')
# -- Plot Gamma and M point dynamic susceptibilities
opt = dict(vmin=-0.01, vmax=0.01, cmap='PuOr')
plt.figure(figsize=(12, 8))
subp = [3, 4, 1]
for q in [[0, 0, 0], [n_k / 2, n_k / 2, 0], [n_k / 2, 0, 0]]:
qidx = bzmesh.index_to_linear(q)
print('-' * 72)
print('q =', q)
print('qidx =', qidx)
subp[-1] += 1
plt.plot(ps.iter, ps.dG_l, 's-')
plt.ylabel('$\max | \Delta G_l |$')
plt.xlabel('Iteration')
plt.semilogy([], [])
plt.subplot(*subp)
subp[-1] += 1
for b, g in p.G_l:
p.G_l[b].data[:] = np.abs(g.data)
oplotr(p.G_l['up'], 'o-', label=None)
plt.ylabel('$| G_l |$')
plt.semilogy([], [])
plt.subplot(*subp)
subp[-1] += 1
oplotr(p.G_tau_raw['up'], alpha=0.75, label='Binned')
oplotr(p.G_tau['up'], label='Legendre')
plt.legend(loc='best', fontsize=8)
plt.ylabel(r'$G(\tau)$')
plt.subplot(*subp)
subp[-1] += 1
oploti(p.sigma_w[0, 0], '.-', label=None)
plt.ylabel(r'$\Sigma(i\omega_n)$')
plt.xlim([-100, 100])
plt.tight_layout()
plt.savefig('figure_sc.svg')
plt.show()