def qes_ft_1d_ltrg(para=None):
if para is None:
para = parameter_qes_gs_by_ed()
hamilts, bath, ob0 = prepare_bath_hamilts(para)
print('Starting ED for the entanglement bath')
dims = [para['d'] for _ in range(para['l_phys'])]
dims = [para['chi']] + dims + [para['chi']]
ob = dict()
solver = EDbasic(dims)
heff = LinearOp((solver.dim_tot, solver.dim_tot),
lambda x: solver.project_all_hamilt(
x, hamilts, para['tau'], para['couplings']))
ob['e_eig'], solver.v = eigs(heff,
k=1,
which='LM',
v0=solver.v.reshape(-1, ).copy())
solver.is_vec = True
ob['e_eig'] = (1 - ob['e_eig']) / para['tau']
ob['mx'], ob['mz'] = solver.observe_magnetizations(para['phys_sites'])
ob['eb'] = solver.observe_bond_energies(
hamilts[0], para['positions_h2'][1:para['num_h2'] - 1, :])
ob['lm'] = solver.calculate_entanglement()
ob['ent'] = entanglement_entropy(ob['lm'])
ob['e_site'] = sum(ob['eb']) / (para['l_phys'] - 1)
ob['corr_xx'] = solver.observe_correlations(para['pos4corr'],
para['op'][1])
ob['corr_zz'] = solver.observe_correlations(para['pos4corr'],
para['op'][3])
for n in range(para['pos4corr'].shape[0]):
p1 = para['pos4corr'][n, 0] - 1
p2 = para['pos4corr'][n, 1] - 1
ob['corr_xx'][n] -= ob['mx'][p1] * ob['mx'][p2]
ob['corr_zz'][n] -= ob['mz'][p1] * ob['mz'][p2]
return bath, solver, ob0, ob
def exact_ground_state(para=None):
if para is None:
para = parameters_ed_ground_state('chain')
hamilt = hamiltonian_heisenberg(para['spin'], para['jx'], para['jy'],
para['jz'], para['hx'] / 2, para['hz'] / 2)
dims = [para['d'] for _ in range(para['l'])]
a = EDbasic(dims)
ob = dict()
dim = para['d']**para['l']
heff = LinearOp((dim, dim), lambda x: a.project_all_hamilt(
x, [hamilt], para['tau'], para['couplings']))
ob['e_eig'], a.v = eigs(heff, k=1, which='LM', v0=a.v.reshape(-1, ).copy())
a.is_vec = True
ob['e_eig'] = (1 - ob['e_eig']) / para['tau']
ob['mx'], ob['mz'] = a.observe_magnetizations(list(range(para['l'])))
ob['eb'] = a.observe_bond_energies(hamilt, para['positions_h2'])
ob['lm'] = a.calculate_entanglement()
ob['ent'] = entanglement_entropy(ob['lm'][-1])
ob['e_site'] = sum(ob['eb']) / para['l']
# ob['e_site'] = sum(ob['eb']) / para['l'] - sum(ob['mx']) * para['hx'] / para['l'] - \
# sum(ob['mz']) * para['hz'] / para['l']
return a, ob
def exact_time_evolution(v0, para=None):
if para is None:
para = parameters_ed_time_evolution('chain')
a = EDbasic(para['d'], para['l'], ini=v0)
hamilt = hamiltonian_heisenberg(para['spin'], para['jx'], para['jy'],
para['jz'], para['hx'] / 2, para['hz'] / 2)
gate = la.expm(1j * para['tau'] * hamilt)
ob = dict()
ob['lm'] = list()
ob['ent'] = list()
ob['mx'] = list()
ob['mz'] = list()
ob['eb'] = list()
ob['e_site'] = list()
time_now = 0
for t in range(para['iterate_time']):
for n in range(para['num_h2']):
a.contract_with_local_matrix(gate,
list(para['positions_h2'][n, :]))
time_now += para['tau']
tmp = time_now / para['ob_dt']
if abs(tmp - round(tmp)) < 1e-9:
mx, mz = a.observe_magnetizations()
ob['mx'].append(mx)
ob['mz'].append(mz)
ob['eb'].append(
a.observe_bond_energies(hamilt, para['positions_h2']))
ob['lm'].append(a.calculate_entanglement())
ob['ent'].append(entanglement_entropy(ob['lm'][-1]))
ob['e_site'].append(
sum(ob['eb'][-1]) / para['l'] +
sum(ob['mx'][-1]) * para['hx'] / para['l'] +
sum(ob['mz'][-1]) * para['hz'] / para['l'])
print('t = ' + str(time_now) + ', Mz = ' +
str(sum(ob['mz']) / a.l))
def qes_1d_ed(para=None):
if para is None:
para = parameter_qes_by_ed()
print('Starting iDMRG for the entanglement bath')
bath_data = opath.join(para['bath_path'], para['bath_exp'])
if para['if_load_bath'] and opath.isfile(bath_data):
print('Bath data found. Load the bath.')
bath, ob0, hamilt = load_pr(bath_data, ['A', 'ob0', 'hamilt'])
else:
print('Bath data not found. Calculate bath by iDMRG.')
hamilt = hamiltonian_heisenberg(para['spin'], para['jxy'], para['jxy'],
para['jz'], para['hx'] / 2,
para['hz'] / 2)
bath, ob0 = dmrg_infinite_size(para, hamilt=hamilt)[:2]
save_pr(para['bath_path'], para['bath_exp'], [bath, ob0, hamilt],
['A', 'ob0', 'hamilt'])
if (bath.is_symme_env is True) and (bath.dmrg_type is 'mpo'):
bath.env[1] = bath.env[0]
print('Preparing the physical-bath Hamiltonians')
qes = QES_1D(para['d'], para['chi'], para['d'] * para['d'], para['l_phys'],
para['tau'])
if bath.dmrg_type is 'mpo':
qes.obtain_physical_gate_tensors(hamilt)
qes.obtain_bath_h(bath.env, 'both')
else:
qes.obtain_bath_h_by_effective_ops_1d(bath.bath_op_onsite,
bath.effective_ops,
bath.hamilt_index)
print('Starting ED for the entanglement bath')
dims = [para['d'] for _ in range(para['l_phys'])]
dims = [para['chi']] + dims + [para['chi']]
hamilts = [hamilt] + qes.hamilt_bath
ob = dict()
solver = EDbasic(dims)
heff = LinearOp((solver.dim_tot, solver.dim_tot),
lambda x: solver.project_all_hamilt(
x, hamilts, para['tau'], para['couplings']))
ob['e_eig'], solver.v = eigs(heff,
k=1,
which='LM',
v0=solver.v.reshape(-1, ).copy())
solver.is_vec = True
ob['e_eig'] = (1 - ob['e_eig']) / para['tau']
ob['mx'], ob['mz'] = solver.observe_magnetizations(para['phys_sites'])
ob['eb'] = solver.observe_bond_energies(
hamilt, para['positions_h2'][1:para['num_h2'] - 1, :])
ob['lm'] = solver.calculate_entanglement()
ob['ent'] = entanglement_entropy(ob['lm'])
ob['e_site'] = sum(ob['eb']) / (para['l_phys'] - 1)
ob['corr_xx'] = solver.observe_correlations(para['pos4corr'],
para['op'][1])
ob['corr_zz'] = solver.observe_correlations(para['pos4corr'],
para['op'][3])
for n in range(para['pos4corr'].shape[0]):
p1 = para['pos4corr'][n, 0] - 1
p2 = para['pos4corr'][n, 1] - 1
ob['corr_xx'][n] -= ob['mx'][p1] * ob['mx'][p2]
ob['corr_zz'][n] -= ob['mz'][p1] * ob['mz'][p2]
return bath, solver, ob0, ob