def example_TEBD_tf_ising_lightcone(L, g, tmax, dt):
print("finite TEBD, real time evolution, transverse field Ising")
print("L={L:d}, g={g:.2f}, tmax={tmax:.2f}, dt={dt:.3f}".format(L=L, g=g, tmax=tmax, dt=dt))
# find ground state with TEBD or DMRG
# E, psi, M = example_TEBD_gs_tf_ising_finite(L, g)
from d_dmrg import example_DMRG_tf_ising_finite
E, psi, M = example_DMRG_tf_ising_finite(L, g)
i0 = L // 2
# apply sigmaz on site i0
SzB = np.tensordot(M.sigmaz, psi.Bs[i0], axes=[1, 1]) # i [i*], vL [i] vR
psi.Bs[i0] = np.transpose(SzB, [1, 0, 2]) # vL i vR
U_bonds = calc_U_bonds(M.H_bonds, 1.j * dt) # (imaginary dt -> realtime evolution)
S = [psi.entanglement_entropy()]
Nsteps = int(tmax / dt + 0.5)
for n in range(Nsteps):
if abs((n * dt + 0.1) % 0.2 - 0.1) < 1.e-10:
print("t = {t:.2f}, chi =".format(t=n * dt), psi.get_chi())
run_TEBD(psi, U_bonds, 1, chi_max=50, eps=1.e-10)
S.append(psi.entanglement_entropy())
import matplotlib.pyplot as plt
plt.figure()
plt.imshow(S[::-1],
vmin=0.,
aspect='auto',
interpolation='nearest',
extent=(0, L - 1., -0.5 * dt, (Nsteps + 0.5) * dt))
plt.xlabel('site $i$')
plt.ylabel('time $t/J$')
plt.ylim(0., tmax)
plt.colorbar().set_label('entropy $S$')
filename = 'c_tebd_lightcone_{g:.2f}.pdf'.format(g=g)
plt.savefig(filename)
print("saved " + filename)
def example_TEBD_tf_ising_lightcone(L, g, tmax, dt, verbose=True):
print("finite TEBD, real time evolution")
print("L={L:d}, g={g:.2f}, tmax={tmax:.2f}, dt={dt:.3f}".format(L=L,
g=g,
tmax=tmax,
dt=dt))
# find ground state with TEBD or DMRG
# E, psi, M = example_TEBD_gs_tf_ising_finite(L, g)
from d_dmrg import example_DMRG_tf_ising_finite
print("(run DMRG to get the groundstate)")
E, psi, M = example_DMRG_tf_ising_finite(L, g, verbose=False)
print("(DMRG finished)")
i0 = L // 2
# apply sigmaz on site i0
psi.apply_local_op(i0, 'Sigmaz', unitary=True)
dt_measure = 0.05
# tebd.Engine makes 'N_steps' steps of `dt` at once; for second order this is more efficient.
tebd_params = {
'order': 2,
'dt': dt,
'N_steps': int(dt_measure // dt),
'trunc_params': {
'chi_max': 50,
'svd_min': 1.e-10,
'trunc_cut': None
},
'verbose': verbose,
}
eng = tebd.Engine(psi, M, tebd_params)
S = [psi.entanglement_entropy()]
for n in range(int(tmax / dt_measure + 0.5)):
eng.run()
S.append(psi.entanglement_entropy())
import matplotlib.pyplot as plt
plt.figure()
plt.imshow(S[::-1],
vmin=0.,
aspect='auto',
interpolation='nearest',
extent=(0, L - 1., -0.5 * dt_measure,
eng.evolved_time + 0.5 * dt_measure))
plt.xlabel('site $i$')
plt.ylabel('time $t/J$')
plt.ylim(0., tmax)
plt.colorbar().set_label('entropy $S$')
filename = 'c_tebd_lightcone_{g:.2f}.pdf'.format(g=g)
plt.savefig(filename)
print("saved " + filename)
