plt.plot(np.arange(len(eec)), eiej, '.')
plt.xlabel('Eigenvector number', fontsize=fsfs)
plt.ylabel(r'$\langle e_i | e_j \rangle$', fontsize=fsfs)
plt.title(r'Orthogonality of eigenvectors $\langle e_i | e_j \rangle$',
fontsize=fsfs)
# plt.title(r'$e_i e^*_i$')
plt.show()
plt.plot(np.arange(len(sum0)), sum0, 'b.-', label='sum of cols')
plt.plot(np.arange(len(sum0)), sum1, 'r.-', label='sum of rows')
plt.title(r'$\sum_{i} |e_i^2|$', fontsize=fsfs)
plt.legend(fontsize=fsfs)
plt.show()
le.plot_complex_matrix(ss, show=True, name=r'$S$', fontsize=fsfs)
le.plot_complex_matrix(nearI - np.identity(len(ss)),
show=True,
name=r'$S S^{\dagger} - I$',
fontsize=fsfs)
#######################################################
# Check that projector is mapping states above to themselves
# for ii in range(len(eigval)):
# if eigval[ii] < omegac:
# plt.plot(np.arange(len(eigvect[:, 0])), np.dot(pp, eigvect[ii, :]), 'b')
# plt.pause(0.01)
# else:
# plt.plot(np.arange(len(eigvect[:, 0])), np.dot(pp, eigvect[ii, :]) - eigvect[ii, :], 'r')
# plt.pause(0.01)
#
output.close()
output = open(meshfn + '/harmonic_diffusivity_sigma.pkl', 'wb')
pickle.dump(SS, output)
output.close()
output = open(meshfn + '/harmonic_diffusivity_sigmax.pkl', 'wb')
pickle.dump(SSx, output)
output.close()
output = open(meshfn + '/harmonic_diffusivity_sigmay.pkl', 'wb')
pickle.dump(SSy, output)
output.close()
###################
# PLOT HEAT FLUX
###################
le.plot_complex_matrix(np.log(SSy),
name=r'$\ln\Sigma_y$',
climvs=[[-1, 2], [-1, 2]],
show=True)
le.plot_complex_matrix(np.log(SSx),
name=r'$\ln\Sigma_x$',
climvs=[[-1, 2], [-1, 2]],
show=True)
le.plot_real_matrix(SS,
name=r'$|\Sigma|^2$',
outpath=meshfn + '/harmonic_diffusivity_sigma',
climv=(0, 1))
le.plot_real_matrix(np.log(SS),
name=r'$\ln|\Sigma|^2$',
outpath=meshfn + '/harmonic_diffusivity_sigmasquared')
le.plot_pcolormesh_scalar(eigval,
eigval,
SS,
U1 = la.inv(U)
D = np.zeros((len(U), len(U)), dtype=complex)
for ii in range(len(eigval)):
ev = eigval[ii]
D[ii, ii] = ev
M = copy.deepcopy(D)
M[M.real < 0] = 0
M[M.real > 0] = 1
P = np.dot(U, np.dot(M, U1))
# CHECK the matrices
le.plot_complex_matrix(P,
name='Projector',
outpath=dataNdir + 'P_matrix.png',
show=False,
close=True)
if args.check:
le.plot_complex_matrix(D,
name='Eigenvalue Matrix',
outpath=dataNdir + 'D_matrix.png',
show=False,
close=True)
le.plot_complex_matrix(M,
name='Cut-Off Eigval Matrix',
outpath=dataNdir + 'M_matrix.png',
show=False,
close=True)
# P is hermitian
le.plot_complex_matrix(P - P.transpose().conjugate(),
# M[M.imag < omegac] = 0
# M[M.imag > omegac] = 1
# Try projecting onto a single state
M = np.zeros_like(D, dtype=float)
M[100, 100] = 1
P = np.dot(U, np.dot(M, U1))
h = np.zeros((len(P), len(P), len(P)), dtype=complex)
######################################################
# CHECK
if check or checkout:
le.plot_complex_matrix(DM,
name='Dynamical Matrix',
outpath=dataNdir + 'DM',
show=check,
close=True)
le.plot_complex_matrix(D,
name='Eigenvalue Matrix',
outpath=dataNdir + 'D',
show=check,
close=True)
le.plot_complex_matrix(M,
name='Cut-Off Eigval Matrix',
outpath=dataNdir + 'M',
show=check,
close=True)
le.plot_complex_matrix(P,
name='Projector',
outpath=dataNdir + 'P',
def twistbcs(lp):
"""Load a periodic lattice from file, twist the BCs by phases theta_twist and phi_twist with vals finely spaced
between 0 and 2pi. Then compute the berry curvature associated with |alpha(theta, phi)>
Example usage:
python haldane_lattice_class.py -twistbcs -N 3 -LT hexagonal -shape square -periodic
Parameters
----------
lp
Returns
-------
"""
lp['periodicBC'] = True
meshfn = le.find_meshfn(lp)
lp['meshfn'] = meshfn
lat = lattice_class.Lattice(lp)
lat.load()
# Make a big array of the eigvals: N x N x thetav x phiv
# thetav = np.arange(0., 2. * np.pi, 0.5)
# phiv = np.arange(0., 2. * np.pi, 0.5)
# First just test for two values of theta and two of phi
thetav = [0., 0.01]
phiv = [0., 0.01]
eigvects = {}
ii = 0
for theta in thetav:
eigvects[ii] = {}
jj = 0
for phi in phiv:
lpnew = copy.deepcopy(lp)
lpnew['theta_twist'] = theta
lpnew['phi_twist'] = phi
hlat = HaldaneLattice(lat, lpnew)
ev, evec = hlat.get_eigval_eigvect(attribute=True)
if ii == 0 and jj == 0:
eigval = copy.deepcopy(ev)
ill = hlat.get_ill()
eigvects[ii][jj] = evec
jj += 1
ii += 1
# Dot the derivs of eigvects together
# Ensure that there is a nonzero-amplitude wannier with matching phase
dtheta = eigvects[1][0] - eigvects[0][0]
dphi = eigvects[0][1] - eigvects[0][0]
thetamov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(thetamov_fn):
# Plot differences
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\phi \psi$')
hlat.lattice.plot_BW_lat(fig=fig,
ax=eig_ax,
save=False,
close=False,
axis_off=False,
title='')
outdir = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dtheta, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving theta ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
phimov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(phimov_fn):
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\phi \psi$')
outdir = dio.prepdir(
hlat.lp['meshfn']) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dphi, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving phi ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
# Check
# print 'shape(dtheta) = ', np.shape(dtheta)
# print 'shape(dphi) = ', np.shape(dphi)
# le.plot_complex_matrix(dtheta, show=True, name='dtheta')
# le.plot_complex_matrix(dphi, show=True, name='dphi')
fig, ax = leplt.initialize_nxmpanel_fig(4, 1, wsfrac=0.6, x0frac=0.3)
# < dphi | dtheta >
dpdt = np.einsum('ij...,ij...->i...', dtheta, dphi.conj())
# < dtheta | dphi >
dtdp = np.einsum('ij...,ij...->i...', dphi, dtheta.conj())
print 'dtdp = ', dtdp
ax[0].plot(np.arange(len(dtdp)), dtdp, '-')
ax[1].plot(np.arange(len(dpdt)), dpdt, '-')
hc = 2. * np.pi * 1j * (dpdt - dtdp)
ax[2].plot(np.arange(len(lat.xy)), hc, '.-')
# Plot cumulative sum
sumhc = np.cumsum(hc)
ax[3].plot(np.arange(len(lat.xy)), sumhc, '.-')
ax[2].set_xlabel(r'Eigvect number')
ax[0].set_ylabel(
r'$\langle \partial_{\theta} \alpha_i | \partial_{\phi} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[1].set_ylabel(
r'$\langle \partial_{\phi} \alpha_i | \partial_{\theta} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[2].set_ylabel(r'$c_H$')
ax[3].set_xlabel(r'Eigvect number')
ax[3].set_ylabel(r'$\sum_{E_\alpha < E_c} c_H$')
outdir = '/Users/npmitchell/Dropbox/Soft_Matter/GPU/twistbc_test/'
dio.ensure_dir(outdir)
print 'saving ', outdir + 'test' + hlat.lp['meshfn_exten'] + '.png'
plt.savefig(outdir + 'test' + hlat.lp['meshfn_exten'] + '.png')
# ### Now do the same thing but with different values of theta, phi
# First just test for two values of theta and two of phi
thetav = [1., 1.01]
phiv = [1., 1.01]
eigvects = {}
ii = 0
for theta in thetav:
eigvects[ii] = {}
jj = 0
for phi in phiv:
lpnew = copy.deepcopy(lp)
lpnew['theta_twist'] = theta
lpnew['phi_twist'] = phi
hlat = HaldaneLattice(lat, lpnew)
ev, evec = hlat.get_eigval_eigvect(attribute=True)
if ii == 0 and jj == 0:
eigval = copy.deepcopy(ev)
ill = hlat.get_ill()
eigvects[ii][jj] = evec
jj += 1
ii += 1
# Dot the derivs of eigvects together
dtheta = eigvects[1][0] - eigvects[0][0]
dphi = eigvects[0][1] - eigvects[0][0]
# Plot differences
thetamov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(thetamov_fn):
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\theta \psi$')
hlat.lattice.plot_BW_lat(fig=fig,
ax=eig_ax,
save=False,
close=False,
axis_off=False,
title='')
outdir = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dtheta, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving theta ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
# Now do phi
phimov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(phimov_fn):
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\phi \psi$')
hlat.lattice.plot_BW_lat(fig=fig,
ax=eig_ax,
save=False,
close=False,
axis_off=False,
title='')
outdir = dio.prepdir(
hlat.lp['meshfn']) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dphi, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving phi ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
# Check
# print 'shape(dtheta) = ', np.shape(dtheta)
# print 'shape(dphi) = ', np.shape(dphi)
# le.plot_complex_matrix(dtheta, show=True, name='dtheta')
# le.plot_complex_matrix(dphi, show=True, name='dphi')
fig, ax = leplt.initialize_nxmpanel_fig(4, 1, wsfrac=0.6, x0frac=0.3)
# < dphi | dtheta >
dpdt = np.einsum('ij...,ij...->i...', dtheta, dphi.conj())
# < dtheta | dphi >
dtdp = np.einsum('ij...,ij...->i...', dphi, dtheta.conj())
print 'dtdp = ', dtdp
ax[0].plot(np.arange(len(dtdp)), dtdp, '-')
ax[1].plot(np.arange(len(dpdt)), dpdt, '-')
hc = 2. * np.pi * 1j * (dpdt - dtdp)
ax[2].plot(np.arange(len(lat.xy)), hc, '.-')
# Plot cumulative sum
sumhc = np.cumsum(hc)
ax[3].plot(np.arange(len(lat.xy)), sumhc, '.-')
ax[2].set_xlabel(r'Eigvect number')
ax[0].set_ylabel(
r'$\langle \partial_{\theta} \alpha_i | \partial_{\phi} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[1].set_ylabel(
r'$\langle \partial_{\phi} \alpha_i | \partial_{\theta} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[2].set_ylabel(r'$c_H$')
ax[3].set_xlabel(r'Eigvect number')
ax[3].set_ylabel(r'$\sum_{E_\alpha < E_c} c_H$')
outdir = '/Users/npmitchell/Dropbox/Soft_Matter/GPU/twistbc_test/'
dio.ensure_dir(outdir)
plt.savefig(outdir + 'test' + hlat.lp['meshfn_exten'] + '_theta1p0.png')
sys.exit()
########################################
# Now test for more theta values, more phi values
thetav = np.arange(0., 0.14, 0.1)
phiv = np.arange(0., 0.14, 0.1)
eigvects = np.zeros((len(lat.xy), len(lat.xy), len(thetav), len(phiv)),
dtype=complex)
ii = 0
for theta in thetav:
jj = 0
for phi in phiv:
lpnew = copy.deepcopy(lp)
lpnew['theta_twist'] = theta
lpnew['phi_twist'] = phi
hlat = HaldaneLattice(lat, lpnew)
ev, evec = hlat.get_eigval_eigvect()
eigvects[:, :, ii, jj] = evec
jj += 1
ii += 1
# Dot the derivs of eigvects together
print 'eigvects = ', eigvects
dtheta = np.diff(eigvects, axis=2)
dphi = np.diff(eigvects, axis=3)
print 'dtheta = ', dtheta
print 'shape(dtheta) = ', np.shape(dtheta)
print 'shape(dphi) = ', np.shape(dphi)
le.plot_complex_matrix(dtheta[:, :, 0, 0], show=True)
le.plot_complex_matrix(dphi[:, :, 0, 0], show=True)
dtheta = dtheta[:, :, :, 0:np.shape(dtheta)[3] - 1]
dphi = dphi[:, :, 0:np.shape(dphi)[2] - 1, :]
print 'shape(dtheta) = ', np.shape(dtheta)
print 'shape(dphi) = ', np.shape(dphi)
for ii in range(np.shape(dtheta)[-1]):
le.plot_complex_matrix(dtheta[:, :, ii, 0], show=True)
fig, ax = leplt.initialize_nxmpanel_fig(3, 1)
for ii in range(np.shape(dphi)[-1]):
for jj in range(np.shape(dphi)[-1]):
# < dphi | dtheta >
dpdt = np.dot(dtheta[:, :, ii, jj], dphi[:, :, ii, jj].conj().T)
# < dtheta | dphi >
dtdp = np.dot(dphi[:, :, ii, jj], dtheta[:, :, ii, jj].conj().T)
print 'np.shape(dpdt) = ', np.shape(dpdt)
print 'np.shape(dtdp) = ', np.shape(dtdp)
ax[0].plot(np.arange(len(dtdp)), dtdp, '-')
ax[1].plot(np.arange(len(dpdt)), dpdt, '-')
hc = 2. * np.pi * 1j * (dpdt - dtdp)
ax[2].plot(np.arange(len(lat.xy)), hc, '.-')
ax[0].set_xlabel(r'$\theta$')
ax[0].set_ylabel(
r'$\langle \partial_{\theta} \alpha_i | \partial_{\phi} \alpha_i \rangle$'
)
ax[1].set_xlabel(r'$\phi$')
ax[1].set_ylabel(
r'$\langle \partial_{\phi} \alpha_i | \partial_{\theta} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[2].set_ylabel(r'$\partial_{\phi} \alpha_i$')
plt.show()
NL = (NLload).astype(np.intc)
KL = (KLload).astype(np.intc)
NP = np.shape(KL)[0]
NN = np.shape(KL)[1]
BL = le.NL2BL(NL, KL)
eigvect, eigval, DM = le.save_normal_modes_haldane(datadir,
xy,
NL,
KL,
BL,
epsilon=epsilon)
np.savetxt(datadir + 'haldane_matrix.txt', DM, delimiter=',')
le.plot_complex_matrix(DM,
name='Dyn. M.',
outpath=datadir + 'haldane_matrix',
show=False,
clear=True)
le.plot_complex_matrix(DM,
name='Dyn. M.',
outpath=datadir + 'chern/haldane/haldane_matrix',
show=False,
clear=True)
with open(datadir + 'eigval_haldane.pkl', "rb") as input_file:
eigval = cPickle.load(input_file)
with open(datadir + 'eigvect_haldane.pkl', "rb") as input_file:
eigvect = cPickle.load(input_file)
# Define projector operator
# First define U such that A = U D U^{-1},
# where D = diag(eigenvals), and A is dynamical matrix