def run_groundstate_xxz(L=30,
Jz=1.,
hz=0.,
conserve='best',
chi_max=50,
Jz_init=None):
model_params = dict(L=L,
Jx=1.,
Jy=1.,
Jz=Jz,
hz=hz,
bc_MPS='finite',
conserve='best',
verbose=1)
result = {}
M = SpinChain(model_params)
result['model'] = 'SpinChain'
result['model_params'] = model_params
result['sites'] = np.arange(L)
result['bonds'] = np.arange(L - 1) + 0.5
psi = MPS.from_product_state(M.lat.mps_sites(), (["up", "down"] * L)[:L])
dmrg_params = {
'trunc_params': {
'chi_max': chi_max,
'svd_min': 1.e-10,
'trunc_cut': None
},
'mixer': True,
'verbose': 1
}
if Jz_init:
# run first time with small hx to break the symmetry
model_params_Jz = model_params.copy()
model_params_Jz['Jz'] = Jz_init
M_Jz = SpinChain(model_params_Jz)
dmrg_params['start_env'] = 10,
run_DMRG(psi, M_Jz, dmrg_params)
# run simulation
t0 = time.time()
info = run_DMRG(psi, M, dmrg_params)
print("DMRG finished after", time.time() - t0, "s")
# save results in output file
result['chi'] = np.array(psi.chi)
result['S'] = np.array(psi.entanglement_entropy())
result['E'] = info['E']
result['sweeps'] = info['sweep_statistics']['sweep']
for key in ['E', 'S', 'max_trunc_err', 'max_E_trunc', 'max_chi']:
result_key = 'sweep_' + key
result[result_key] = np.array(info['sweep_statistics'][key])
return result
def run(Jzs):
L = 2
model_params = dict(L=L,
Jx=1.,
Jy=1.,
Jz=1.,
bc_MPS='infinite',
conserve='Sz',
verbose=0)
chi = 300
dmrg_params = dict(trunc_params={
'chi_max': chi,
'svd_min': 1.e-10,
'trunc_cut': None
},
update_env=20,
start_env=20,
max_E_err=0.0001,
max_S_err=0.0001,
verbose=1,
mixer=True)
M = SpinChain(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), (["up", "down"] * L)[:L],
M.lat.bc_MPS)
np.set_printoptions(linewidth=120)
corr_length = []
for Jz in Jzs:
print("-" * 80)
print("Jz =", Jz)
print("-" * 80)
model_params['Jz'] = Jz
M = SpinChain(model_params)
run_DMRG(psi, M, dmrg_params)
corr_length.append(psi.correlation_length(tol_ev0=1.e-3))
print("corr. length", corr_length[-1])
print("<Sz>", psi.expectation_value('Sz'))
corr_length = np.array(corr_length)
results = {
'model_params': model_params,
'dmrg_params': dmrg_params,
'Jzs': Jzs,
'corr_length': corr_length,
'eval_transfermatrix': np.exp(-1. / corr_length)
}
return results
xxz_pars = dict(L=4, Jxx=1., Jz=1., hz=0.0, bc_MPS='finite')
M = XXZChain(xxz_pars)
ED = ExactDiag(M, [0])
ED.build_full_H_from_mpo()
# ED.build_full_H_from_bonds() # whatever you prefer
print("start diagonalization")
ED.full_diagonalization()
psi_ED = ED.groundstate()
print("psi_ED =", psi_ED)
print("start DMRG")
product_state = [0, 1] * (xxz_pars['L'] // 2) # this selects a charge sector!
psi_DMRG = MPS.from_product_state(M.lat.mps_sites(), product_state)
res = run_DMRG(psi_DMRG, M, {'verbose': 0})
# first way to compare ED with DMRG: convert MPS to ED vector
psi_DMRG_full = ED.mps_to_full(psi_DMRG)
print("psi_DMRG_full =", psi_DMRG_full)
ov = abs(npc.inner(psi_ED, psi_DMRG_full, do_conj=True))
print("|<psi_ED|psi_DMRG>| =", ov)
assert (abs(ov - 1.) < 1.e-13)
# second way: convert ED vector to MPS
psi_ED_mps = ED.full_to_mps(psi_ED)
ov = psi_ED_mps.overlap(psi_DMRG)
print("|<psi_ED_mps|psi_DMRG>| =", abs(ov))
assert (abs(abs(ov) - 1.) < 1.e-13)
# -> advantange: expectation_value etc. of MPS are available!
print("<Sz> =", psi_ED_mps.expectation_value('Sz'))
def run(Jzs):
L = 2
bc = 'infinite'
model_params = dict(L=L,
Jx=1.,
Jy=1.,
Jz=1.,
bc_MPS=bc,
conserve='Sz',
verbose=0)
chi = 300
dmrg_params = dict(trunc_params={
'chi_max': chi,
'svd_min': 1.e-10,
'trunc_cut': None
},
update_env=20,
start_env=20,
max_E_err=0.0001,
max_S_err=0.0001,
verbose=1,
mixer=True) # TODO: mixer?
M = SpinChain(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), [1, 0] * (L // 2), bc)
# B = np.zeros([2, 2, 2])
# B[0, 0, 0] = B[1, 1, 1] = 1.
# psi = MPS.from_Bflat(M.lat.mps_sites(), [B]*L, bc=bc)
np.set_printoptions(linewidth=120)
corr_length = []
for Jz in Jzs:
print("-" * 80)
print("Jz =", Jz)
print("-" * 80)
model_params['Jz'] = Jz
M = SpinChain(model_params)
# # psi = MPS.from_product_state(M.lat.mps_sites(), [1, 1]*(L//2), bc)
# B = np.zeros([2, 2, 2])
# B[0, 0, 0] = B[1, 1, 1] = 1.
# psi = MPS.from_Bflat(M.lat.mps_sites(), [B]*L, bc=bc)
run_DMRG(psi, M, dmrg_params)
if bc == 'infinite':
# T = TransferMatrix(psi, psi, charge_sector=None)
# E, V = T.eigenvectors(4, which='LM')
# chi = psi.chi[0]
# print V[0].to_ndarray().reshape([chi, chi])[:5, :5] * chi**0.5
# if len(V) > 1:
# print V[1].to_ndarray().reshape([chi, chi])[:5, :5] * chi**0.5
# print "chi:", psi.chi
# print "eigenvalues transfermatrix:", E
# print "norm_test:", psi.norm_test()
corr_length.append(
psi.correlation_length(charge_sector=0, tol_ev0=1.e-3))
print("corr. length", corr_length[-1])
print("corr. fct.",
psi.correlation_function('Sz', 'Sz', sites1=[0], sites2=6))
print("<Sz>", psi.expectation_value('Sz'))
else:
print(psi.correlation_function('Sz', 'Sz'))
corr_length = np.array(corr_length)
results = {
'model_params': model_params,
'dmrg_params': dmrg_params,
'Jzs': Jzs,
'corr_length': corr_length,
'eval_transfermatrix': np.exp(-1. / corr_length)
}
return results