def init_mps(self):
tentative_mpo = Mpo(self.mol_list)
if self.temperature == 0:
gs_mp = Mps.gs(self.mol_list, max_entangled=False)
if self.dissipation != 0:
gs_mp = MpDm.from_mps(gs_mp)
else:
gs_mp = MpDm.max_entangled_gs(self.mol_list)
# subtract the energy otherwise might cause numeric error because of large offset * dbeta
energy = Quantity(gs_mp.expectation(tentative_mpo))
mpo = Mpo(self.mol_list, offset=energy)
tp = ThermalProp(gs_mp, mpo, exact=True, space="GS")
tp.evolve(None, len(gs_mp), self.temperature.to_beta() / 2j)
gs_mp = tp.latest_mps
init_mp = self.create_electron(gs_mp)
if self.dissipation != 0:
init_mp = MpDmFull.from_mpdm(init_mp)
energy = Quantity(init_mp.expectation(tentative_mpo))
self.mpo = Mpo(self.mol_list, offset=energy)
logger.info(f"mpo bond dims: {self.mpo.bond_dims}")
logger.info(f"mpo physical dims: {self.mpo.pbond_list}")
if self.dissipation != 0:
self.mpo = SuperLiouville(self.mpo, self.dissipation)
init_mp.canonicalise()
init_mp.evolve_config = self.evolve_config
# init the compress config if not using threshold and not set
if self.compress_config.criteria is not CompressCriteria.threshold\
and self.compress_config.max_dims is None:
self.compress_config.set_bonddim(length=len(init_mp) + 1)
init_mp.compress_config = self.compress_config
# init_mp.invalidate_cache()
return init_mp
def init_mps(self):
tentative_mpo = Mpo(self.model)
if self.temperature == 0:
gs_mp = Mps.ground_state(self.model, max_entangled=False)
else:
if self._defined_output_path:
gs_mp = load_thermal_state(self.model, self._thermal_dump_path)
else:
gs_mp = None
if gs_mp is None:
gs_mp = MpDm.max_entangled_gs(self.model)
# subtract the energy otherwise might cause numeric error because of large offset * dbeta
energy = Quantity(gs_mp.expectation(tentative_mpo))
mpo = Mpo(self.model, offset=energy)
tp = ThermalProp(gs_mp, mpo, exact=True, space="GS")
tp.evolve(None, max(20, len(gs_mp)), self.temperature.to_beta() / 2j)
gs_mp = tp.latest_mps
if self._defined_output_path:
gs_mp.dump(self._thermal_dump_path)
init_mp = self.create_electron(gs_mp)
energy = Quantity(init_mp.expectation(tentative_mpo))
self.mpo = Mpo(self.model, offset=energy)
logger.info(f"mpo bond dims: {self.mpo.bond_dims}")
logger.info(f"mpo physical dims: {self.mpo.pbond_list}")
init_mp.evolve_config = self.evolve_config
init_mp.compress_config = self.compress_config
if self.evolve_config.is_tdvp:
init_mp = init_mp.expand_bond_dimension(self.mpo)
init_mp.canonicalise()
return init_mp
def test_dynamics(dissipation, dt, nsteps):
tentative_mpo = Mpo(band_limit_mol_list)
gs_mp = MpDm.max_entangled_gs(band_limit_mol_list)
# subtract the energy otherwise might cause numeric error because of large offset * dbeta
energy = Quantity(gs_mp.expectation(tentative_mpo))
mpo = Mpo(band_limit_mol_list, offset=energy)
tp = ThermalProp(gs_mp, mpo, exact=True, space="GS")
tp.evolve(None, 50, low_t.to_beta() / 2j)
gs_mp = tp.latest_mps
center_mol_idx = band_limit_mol_list.mol_num // 2
creation_operator = Mpo.onsite(
band_limit_mol_list, r"a^\dagger", mol_idx_set={center_mol_idx}
)
mpdm = creation_operator.apply(gs_mp)
mpdm_full = MpDmFull.from_mpdm(mpdm)
# As more compression is involved higher threshold is necessary
mpdm_full.compress_config = CompressConfig(threshold=1e-4)
liouville = SuperLiouville(mpo, dissipation)
r_square_list = [calc_r_square(mpdm_full.e_occupations)]
time_series = [0]
for i in range(nsteps - 1):
logger.info(mpdm_full)
mpdm_full = mpdm_full.evolve(liouville, dt)
r_square_list.append(calc_r_square(mpdm_full.e_occupations))
time_series.append(time_series[-1] + dt)
time_series = np.array(time_series)
if dissipation == 0:
assert np.allclose(get_analytical_r_square(time_series), r_square_list, rtol=1e-2, atol=1e-3)
else:
# not much we can do, just basic sanity check
assert (np.array(r_square_list)[1:] < get_analytical_r_square(time_series)[1:]).all()
def init_mps(self):
# first try to load
if self._defined_output_path:
mpdm = load_thermal_state(self.model, self._thermal_dump_path)
else:
mpdm = None
# then try to calculate
if mpdm is None:
i_mpdm = MpDm.max_entangled_ex(self.model)
i_mpdm.compress_config = self.compress_config
if self.job_name is None:
job_name = None
else:
job_name = self.job_name + "_thermal_prop"
tp = ThermalProp(i_mpdm, self.h_mpo, evolve_config=self.ievolve_config, dump_dir=self.dump_dir, job_name=job_name)
# only propagate half beta
tp.evolve(None, self.insteps, self.temperature.to_beta() / 2j)
mpdm = tp.latest_mps
if self._defined_output_path:
mpdm.dump(self._thermal_dump_path)
mpdm.compress_config = self.compress_config
e = mpdm.expectation(self.h_mpo)
self.h_mpo = Mpo(self.model, offset=Quantity(e))
mpdm.evolve_config = self.evolve_config
logger.debug("Applying current operator")
ket_mpdm = self.j_oper.contract(mpdm).canonical_normalize()
bra_mpdm = mpdm.copy()
if self.j_oper2 is None:
return BraKetPair(bra_mpdm, ket_mpdm, self.j_oper)
else:
logger.debug("Applying the second current operator")
ket_mpdm2 = self.j_oper2.contract(mpdm).canonical_normalize()
return BraKetPair(bra_mpdm, ket_mpdm, self.j_oper), BraKetPair(bra_mpdm, ket_mpdm2, self.j_oper2)
def f(mol_list, run_qutip=True):
tentative_mpo = Mpo(mol_list)
init_mps = (Mpo.onsite(mol_list, r"a^\dagger", mol_idx_set={0}) @ Mps.gs(
mol_list, False)).expand_bond_dimension(hint_mpo=tentative_mpo)
init_mpdm = MpDm.from_mps(init_mps).expand_bond_dimension(
hint_mpo=tentative_mpo)
e = init_mps.expectation(tentative_mpo)
mpo = Mpo(mol_list, offset=Quantity(e))
if run_qutip:
# calculate result in ZT. FT result is exactly the same
TIME_LIMIT = 10
QUTIP_STEP = 0.01
N_POINTS = TIME_LIMIT / QUTIP_STEP + 1
qutip_time_series = np.linspace(0, TIME_LIMIT, N_POINTS)
init = qutip.Qobj(init_mps.full_wfn(),
[qutip_h.dims[0], [1] * len(qutip_h.dims[0])])
# the result is not exact and the error scale is approximately 1e-5
res = qutip.sesolve(qutip_h - e,
init,
qutip_time_series,
e_ops=[c.dag() * c for c in qutip_clist])
qutip_expectations = np.array(res.expect).T
return qutip_expectations, QUTIP_STEP, init_mps, init_mpdm, mpo
else:
return init_mps, init_mpdm, mpo
def test_from_mps():
gs = Mps.random(parameter.holstein_model, 1, 20)
gs_mpdm = MpDm.from_mps(gs)
assert np.allclose(gs.e_occupations, gs_mpdm.e_occupations)
gs = gs.canonicalise()
gs_mpdm = gs_mpdm.canonicalise()
assert np.allclose(gs.e_occupations, gs_mpdm.e_occupations)
def __init__(
self,
init_mpdm: MpDm,
h_mpo: Mpo,
exact: bool = False,
space: str = "GS",
evolve_config: EvolveConfig = None,
dump_mps: bool = False,
dump_dir: str = None,
job_name: str = None,
properties: Property = None,
auto_expand: bool = True,
):
self.init_mpdm: MpDm = init_mpdm.canonicalise()
self.h_mpo = h_mpo
self.exact = exact
assert space in ["GS", "EX"]
self.space = space
self.energies = []
self._e_occupations_array = []
self._ph_occupations_array = []
self._vn_entropy_array = []
self.properties = properties
self.auto_expand = auto_expand
super().__init__(evolve_config=evolve_config,
dump_mps=dump_mps,
dump_dir=dump_dir,
job_name=job_name)
def test_FT_dynamics_hybrid_TDDMRG_TDH(n_dmrg_phs, scheme):
mol_list = parameter_PBI.construct_mol(4, n_dmrg_phs, 10 - n_dmrg_phs).switch_scheme(scheme)
mpdm = MpDm.max_entangled_gs(mol_list)
tentative_mpo = Mpo(mol_list)
temperature = Quantity(2000, "K")
tp = ThermalProp(mpdm, tentative_mpo, exact=True, space="GS")
tp.evolve(None, 1, temperature.to_beta() / 2j)
mpdm = (
Mpo.onsite(mol_list, r"a^\dagger", mol_idx_set={0}).apply(tp.latest_mps).normalize(1.0)
)
mpdm.compress_config = CompressConfig(threshold=5e-4)
offset = mpdm.expectation(tentative_mpo)
mpo = Mpo(mol_list, offset=Quantity(offset, "a.u."))
# do the evolution
# nsteps = 90 # too many steps, may take hours to finish
nsteps = 40
dt = 10.0
occ = [mpdm.e_occupations]
for i in range(nsteps):
mpdm = mpdm.evolve(mpo, dt)
occ.append(mpdm.e_occupations)
# make it compatible with std data
occ = np.array(occ[:nsteps]).transpose()
with open(os.path.join(cur_dir, "FT_occ" + str(n_dmrg_phs) + ".npy"), "rb") as f:
std = np.load(f)
assert np.allclose(occ[:, :nsteps], std[:, :nsteps], atol=1e-3, rtol=1e-3)
def init_mps(self):
mmax = self.optimize_config.procedure[0][0]
i_mps = Mps.random(self.h_mpo.model, self.nexciton, mmax, 1)
i_mps.optimize_config = self.optimize_config
energy, i_mps = gs.optimize_mps(i_mps, self.h_mpo)
if self.spectratype == "emi":
operator = "a"
else:
operator = r"a^\dagger"
dipole_mpo = Mpo.onsite(self.model, operator, dipole=True)
if self.temperature != 0:
beta = self.temperature.to_beta()
# print "beta=", beta
# thermal_mpo = Mpo.exact_propagator(self.model, -beta / 2.0, space=self.space1, shift=self.shift1)
# ket_mps = thermal_mpo.apply(i_mps)
# ket_mps.normalize()
# no test, don't know work or not
i_mpdm = MpDm.from_mps(i_mps)
tp = ThermalProp(i_mpdm, self.h_mpo, exact=True, space=self.space1)
tp.evolve(None, 1, beta / 2j)
ket_mps = tp.latest_mps
else:
ket_mps = i_mps
a_ket_mps = dipole_mpo.apply(ket_mps, canonicalise=True)
a_ket_mps.canonical_normalize()
if self.temperature != 0:
a_bra_mps = ket_mps.copy()
else:
a_bra_mps = a_ket_mps.copy()
return BraKetPair(a_bra_mps, a_ket_mps)
def test_thermal_prop(adaptive, evolve_method):
model = parameter.holstein_model
init_mps = MpDm.max_entangled_ex(model)
mpo = Mpo(model)
beta = Quantity(298, "K").to_beta()
evolve_time = beta / 2j
evolve_config = EvolveConfig(evolve_method,
adaptive=adaptive,
guess_dt=0.1 / 1j)
if adaptive:
nsteps = 1
else:
nsteps = 100
if evolve_method == EvolveMethod.tdvp_mu_vmf:
nsteps = 20
evolve_config.ivp_rtol = 1e-3
evolve_config.ivp_atol = 1e-6
evolve_config.reg_epsilon = 1e-8
init_mps.compress_config.bond_dim_max_value = 12
dbeta = evolve_time / nsteps
tp = ThermalProp(init_mps, mpo, evolve_config=evolve_config)
tp.evolve(evolve_dt=dbeta, nsteps=nsteps)
# MPO, HAM, Etot, A_el = mps.construct_hybrid_Ham(mpo, debug=True)
# exact A_el: 0.20896541050347484, 0.35240029674394463, 0.4386342927525734
# exact internal energy: 0.0853388060014744
etot_std = 0.0853388 + parameter.holstein_model.gs_zpe
occ_std = [0.20896541050347484, 0.35240029674394463, 0.4386342927525734]
rtol = 5e-3
assert np.allclose(tp.e_occupations_array[-1], occ_std, rtol=rtol)
assert np.allclose(tp.energies[-1], etot_std, rtol=rtol)
def test_svd_compress(comp, mp):
if mp == "mpo":
mps = Mpo(holstein_model)
M = 22
else:
mps = Mps.random(holstein_model, 1, 10)
if mp == "mpdm":
mps = MpDm.from_mps(mps)
mps.canonicalise().normalize()
M = 36
if comp:
mps = mps.to_complex(inplace=True)
print(f"{mps}")
mpo = Mpo(holstein_model)
if comp:
mpo = mpo.scale(-1.0j)
print(f"{mpo.bond_dims}")
std_mps = mpo.apply(mps, canonicalise=True).canonicalise()
print(f"std_mps: {std_mps}")
mps.compress_config.bond_dim_max_value = M
mps.compress_config.criteria = CompressCriteria.fixed
svd_mps = mpo.contract(mps)
dis = svd_mps.distance(std_mps) / std_mps.dmrg_norm
print(f"svd_mps: {svd_mps}, dis: {dis}")
assert np.allclose(dis, 0.0, atol=1e-3)
assert np.allclose(svd_mps.dmrg_norm, std_mps.dmrg_norm, atol=1e-4)
def test_thermal_equilibrium(periodic):
if periodic:
# define properties
# periodic case
prop_mpos = ops.e_ph_static_correlation(mol_list, periodic=True)
prop_strs = list(prop_mpos.keys())
prop_strs.append("e_rdm")
prop = Property(prop_strs, prop_mpos)
else:
# non-periodic case (though actually periodic)
prop_mpos = {}
for imol in range(nmols):
prop_mpo = ops.e_ph_static_correlation(mol_list, imol=imol)
prop_mpos.update(prop_mpo)
prop_strs = list(prop_mpos.keys())
prop_strs.append("e_rdm")
prop = Property(prop_strs, prop_mpos)
beta = Quantity(1500., "K").to_beta()
logger.info(f"beta:{beta}")
nsteps = 1
dbeta = beta / nsteps / 2j
evolve_config = EvolveConfig(method=EvolveMethod.prop_and_compress, adaptive=True,
adaptive_rtol=1e-4, guess_dt=0.1/1j)
init_mpdm = MpDm.max_entangled_ex(mol_list)
#init_mpdm.compress_config.bond_dim_max_value=10
init_mpdm.compress_config.threshold = 1e-4
td = ThermalProp(init_mpdm, mpo, evolve_config=evolve_config,
dump_dir=dump_dir, job_name=job_name, properties=prop)
td.evolve(dbeta, nsteps=nsteps)
if periodic:
def combine(local_prop):
res = []
for dis in range(nmols):
res.append(local_prop.prop_res["S_"+str(dis)+"_0"][-1])
return res
else:
def combine(local_prop):
e_ph_static_corr = []
for dis in range(nmols):
res = 0.
for i in range(nmols):
res = res + np.array(local_prop.prop_res["S_"+str(i)+"_"+str((i+dis)%nmols)+"_0"][-1])
e_ph_static_corr.append(res)
return e_ph_static_corr
assert np.allclose(td.properties.prop_res["e_rdm"][-1], thermal_std["e_rdm"])
assert np.allclose(combine(td.properties), thermal_std["e_ph_static_corr"])
# directly calculate properties
mpdm = td.latest_mps
prop.calc_properties(mpdm, None)
assert np.allclose(prop.prop_res["e_rdm"][-1], prop.prop_res["e_rdm"][-2])
def test_mpo():
gs_dm = MpDm.max_entangled_gs(mol_list)
beta = Quantity(10, "K").to_beta()
tp = ThermalProp(gs_dm, Mpo(gs_dm.mol_list), exact=True, space="GS")
tp.evolve(None, 500, beta / 1j)
gs_dm = tp.latest_mps
mp = creation_operator.apply(gs_dm)
check_property(mp)
def init_mps(self):
beta = self.temperature.to_beta()
self.h_mpo = Mpo(self.mol_list)
if self.spectratype == "abs":
dipole_mpo = Mpo.onsite(self.mol_list, r"a^\dagger", dipole=True)
i_mpo = MpDm.max_entangled_gs(self.mol_list)
tp = ThermalProp(i_mpo, self.h_mpo, exact=True, space='GS')
tp.evolve(None, 1, beta / 2j)
ket_mpo = tp.latest_mps
else:
impo = MpDm.max_entangled_ex(self.mol_list)
dipole_mpo = Mpo.onsite(self.mol_list, "a", dipole=True)
if self.job_name is None:
job_name = None
else:
job_name = self.job_name + "_thermal_prop"
impo.compress_config = self.compress_config
tp = ThermalProp(impo,
self.h_mpo,
evolve_config=self.evolve_config,
dump_dir=self.dump_dir,
job_name=job_name)
self._defined_output_path = tp._defined_output_path
if tp._defined_output_path:
try:
logger.info(
f"load density matrix from {self._thermal_dump_path}")
ket_mpo = MpDm.load(self.mol_list, self._thermal_dump_path)
logger.info(f"density matrix loaded: {ket_mpo}")
except FileNotFoundError:
logger.debug(f"no file found in {self._thermal_dump_path}")
tp.evolve(None, self.insteps, beta / 2j)
ket_mpo = tp.latest_mps
ket_mpo.dump(self._thermal_dump_path)
self.a_ket_mpo = dipole_mpo.apply(ket_mpo, canonicalise=True)
self.cv_mpo = Mpo.finiteT_cv(self.mol_list,
1,
self.m_max,
self.spectratype,
percent=1.0)
self.cv_mps = self.cv_mpo
def init_mps_abs(self):
dipole_mpo = Mpo.onsite(self.mol_list, r"a^\dagger", dipole=True)
i_mpo = MpDm.max_entangled_gs(self.mol_list)
beta = self.temperature.to_beta()
tp = ThermalProp(i_mpo, self.h_mpo, exact=True, space="GS")
tp.evolve(None, 1, beta / 2j)
ket_mpo = tp.latest_mps
ket_mpo.evolve_config = self.evolve_config
a_ket_mpo = dipole_mpo.apply(ket_mpo, canonicalise=True)
a_ket_mpo.canonical_normalize()
a_bra_mpo = a_ket_mpo.copy()
return BraKetPairAbsFiniteT(a_bra_mpo, a_ket_mpo)
def test_ft_init_state():
ph = Phonon.simple_phonon(Quantity(1), Quantity(1), 10)
mol_list = MolList([Mol(Quantity(0), [ph])], Quantity(0), scheme=3)
temperature = Quantity(0.1)
mpo = Mpo(mol_list)
init_mpdm = MpDm.max_entangled_ex(mol_list)
tp = ThermalProp(init_mpdm, mpo, space="EX", exact=True)
tp.evolve(nsteps=20, evolve_time=temperature.to_beta() / 2j)
ct = ChargeTransport(mol_list, temperature=temperature)
tp_mpdm = MpDmFull.from_mpdm(tp.latest_mps)
ct_mpdm = MpDmFull.from_mpdm(ct.latest_mps)
assert tp_mpdm.angle(ct_mpdm) == pytest.approx(1)
def init_b_mpo(self):
# get the right hand site vector b, Ax=b
# b = -eta * dipole * \psi_0
# only support Holstien model 0/1 exciton manifold
beta = self.temperature.to_beta()
if self.spectratype == "abs":
dipole_mpo = Mpo.onsite(self.model, r"a^\dagger", dipole=True)
i_mpo = MpDm.max_entangled_gs(self.model)
tp = ThermalProp(i_mpo, self.h_mpo, exact=True, space='GS')
tp.evolve(None, 1, beta / 2j)
ket_mpo = tp.latest_mps
elif self.spectratype == "emi":
dipole_mpo = Mpo.onsite(self.model, "a", dipole=True)
if self._defined_output_path:
ket_mpo = \
load_thermal_state(self.model, self._thermal_dump_path)
else:
ket_mpo = None
if ket_mpo is None:
impo = MpDm.max_entangled_ex(self.model)
impo.compress_config = self.compress_config
if self.job_name is None:
job_name = None
else:
job_name = self.job_name + "_thermal_prop"
tp = ThermalProp(impo,
self.h_mpo,
evolve_config=self.evolve_config,
dump_dir=self.dump_dir,
job_name=job_name)
tp.evolve(None, self.insteps, beta / 2j)
ket_mpo = tp.latest_mps
if self._defined_output_path:
ket_mpo.dump(self._thermal_dump_path)
else:
assert False
ket_mpo = dipole_mpo.apply(ket_mpo.scale(-self.eta))
return ket_mpo, None
def init_mps(self):
# first try to load
if self._defined_output_path:
try:
logger.info(f"Try load from {self._thermal_dump_path}")
mpdm = MpDm.load(self.mol_list, self._thermal_dump_path)
logger.info(f"Init mpdm loaded: {mpdm}")
mpdm.compress_config = self.compress_config
except FileNotFoundError:
logger.debug(f"No file found in {self._thermal_dump_path}")
mpdm = None
else:
mpdm = None
# then try to calculate
if mpdm is None:
i_mpdm = MpDm.max_entangled_ex(self.mol_list)
i_mpdm.compress_config = self.compress_config
if self.job_name is None:
job_name = None
else:
job_name = self.job_name + "_thermal_prop"
tp = ThermalProp(i_mpdm,
self.h_mpo,
evolve_config=self.ievolve_config,
dump_dir=self.dump_dir,
job_name=job_name)
# only propagate half beta
tp.evolve(None, self.insteps, self.temperature.to_beta() / 2j)
mpdm = tp.latest_mps
if self._defined_output_path:
mpdm.dump(self._thermal_dump_path)
self.impdm = mpdm
e = mpdm.expectation(self.h_mpo)
self.h_mpo = Mpo(self.mol_list, offset=Quantity(e))
mpdm.evolve_config = self.evolve_config
ket_mpdm = self.j_oper.contract(mpdm).canonical_normalize()
bra_mpdm = mpdm.copy()
return BraKetPair(bra_mpdm, ket_mpdm, self.j_oper)
def test_environ_multi_mpo(mpdm):
mps = Mps.random(holstein_model, 1, 10)
if mpdm:
mps = MpDm.from_mps(mps)
mpo = Mpo(holstein_model)
mps = mps.evolve(mpo, 10)
environ = Environ(mps, mpo)
environ_multi_mpo = Environ(mps, [mpo])
for i in range(len(mps) - 1):
l = environ.read("L", i)
r = environ.read("R", i + 1)
l2 = environ_multi_mpo.read("L", i)
r2 = environ_multi_mpo.read("R", i + 1)
assert np.allclose(asnumpy(l), asnumpy(l2))
assert np.allclose(asnumpy(r), asnumpy(r2))
def init_mps_emi(self):
dipole_mpo = Mpo.onsite(self.mol_list, "a", dipole=True)
i_mpo = MpDm.max_entangled_ex(self.mol_list)
# only propagate half beta
tp = ThermalProp(i_mpo, self.h_mpo)
tp.evolve(None, self.insteps, self.temperature.to_beta() / 2j)
ket_mpo = tp.latest_mps
ket_mpo.evolve_config = self.evolve_config
# e^{\-beta H/2} \Psi
dipole_mpo_dagger = dipole_mpo.conj_trans()
dipole_mpo_dagger.build_empty_qn()
a_ket_mpo = ket_mpo.apply(dipole_mpo_dagger, canonicalise=True)
a_ket_mpo.canonical_normalize()
a_bra_mpo = a_ket_mpo.copy()
return BraKetPairEmiFiniteT(a_bra_mpo, a_ket_mpo)
def init_mps_emi(self):
dipole_mpo = Mpo.onsite(self.mol_list, "a", dipole=True)
i_mpo = MpDm.max_entangled_ex(self.mol_list)
i_mpo.compress_config = self.icompress_config
if self.job_name is None:
job_name = None
else:
job_name = self.job_name + "_thermal_prop"
# only propagate half beta
tp = ThermalProp(i_mpo,
self.h_mpo,
evolve_config=self.ievolve_config,
dump_dir=self.dump_dir,
job_name=job_name)
if tp._defined_output_path:
try:
logger.info(
f"load density matrix from {self._thermal_dump_path}")
ket_mpo = MpDm.load(self.mol_list, self._thermal_dump_path)
logger.info(f"density matrix loaded:{ket_mpo}")
except FileNotFoundError:
logger.debug(f"no file found in {self._thermal_dump_path}")
tp.evolve(None, self.insteps, self.temperature.to_beta() / 2j)
ket_mpo = tp.latest_mps
ket_mpo.dump(self._thermal_dump_path)
else:
tp.evolve(None, self.insteps, self.temperature.to_beta() / 2j)
ket_mpo = tp.latest_mps
ket_mpo.evolve_config = self.evolve_config
# e^{\-beta H/2} \Psi
dipole_mpo_dagger = dipole_mpo.conj_trans()
dipole_mpo_dagger.build_empty_qn()
a_ket_mpo = ket_mpo.apply(dipole_mpo_dagger, canonicalise=True)
a_ket_mpo.canonical_normalize()
a_bra_mpo = a_ket_mpo.copy()
return BraKetPairEmiFiniteT(a_bra_mpo, a_ket_mpo)
def test_variational_compress(comp, mp):
if mp == "mpo":
mps = Mpo(holstein_model)
M = 20
else:
mps = Mps.random(holstein_model, 1, 10)
if mp == "mpdm":
mps = MpDm.from_mps(mps)
mps.canonicalise().normalize()
M = 36
if comp:
mps = mps.to_complex(inplace=True)
print(f"{mps}")
mpo = Mpo(holstein_model)
if comp:
mpo = mpo.scale(-1.0j)
print(f"{mpo.bond_dims}")
std_mps = mpo.apply(mps, canonicalise=True).canonicalise()
print(f"std_mps: {std_mps}")
# 2site algorithm
mps.compress_config.vprocedure = [[M, 1.0], [M, 0.2], [M, 0.1]] + [
[M, 0],
] * 10
mps.compress_config.vmethod = "2site"
var_mps = mps.variational_compress(mpo, guess=None)
dis = var_mps.distance(std_mps) / std_mps.dmrg_norm
print(f"var2_mps: {var_mps}, dis: {dis}")
assert np.allclose(dis, 0.0, atol=1e-4)
assert np.allclose(var_mps.dmrg_norm, std_mps.dmrg_norm, atol=1e-4)
# 1site algorithm with 2site result as a guess
# 1site algorithm is easy to be trapped in a local minimum
var_mps.compress_config.vprocedure = [
[M, 0],
] * 10
var_mps.compress_config.vmethod = "1site"
var_mps = mps.variational_compress(mpo, guess=var_mps)
dis = var_mps.distance(std_mps) / std_mps.dmrg_norm
print(f"var1_mps: {var_mps}, dis: {dis}")
assert np.allclose(dis, 0.0, atol=1e-4)
assert np.allclose(var_mps.dmrg_norm, std_mps.dmrg_norm, atol=1e-4)
def load_thermal_state(mol_list, path: str):
"""
Load thermal propagated state from disk. Return None if the file is not found.
Args:
mol_list (:class:`MolList`): system information
path (str): the path to load thermal state from. Should be an `npz` file.
Returns: Loaded MpDm
"""
try:
logger.info(f"Try load from {path}")
mpdm = MpDm.load(mol_list, path)
logger.info(f"Init mpdm loaded: {mpdm}")
except FileNotFoundError:
logger.info(f"No file found in {path}")
mpdm = None
return mpdm
def test_bogoliubov():
# REF: JCP, 2016, 145, 224101
evolve_config = EvolveConfig(EvolveMethod.tdvp_ps)
# evolve_config = EvolveConfig()
omega = 1
D = 1
nlevel = 10
T = Quantity(1)
ph1 = Phonon.simple_phonon(Quantity(omega), Quantity(D), nlevel)
mol1 = Mol(Quantity(0), [ph1])
mlist = MolList([mol1] * 2, Quantity(1), scheme=4)
mpdm1 = MpDm.max_entangled_gs(mlist)
mpdm1.evolve_config = evolve_config
mpo1 = Mpo(mlist)
tp = ThermalProp(mpdm1, mpo1, exact=True)
tp.evolve(nsteps=20, evolve_time=T.to_beta() / 2j)
mpdm2 = tp.latest_mps
e1 = mpdm2.expectation(mpo1)
mpdm3 = (Mpo.onsite(mlist, r"a^\dagger", False, {0})
@ mpdm2).expand_bond_dimension(mpo1)
es1 = [mpdm3.e_occupations]
for i in range(40):
mpdm3 = mpdm3.evolve(mpo1, 0.1)
es1.append(mpdm3.e_occupations)
theta = np.arctanh(np.exp(-T.to_beta() * omega / 2))
ph2 = Phonon.simple_phonon(Quantity(omega), Quantity(D * np.cosh(theta)),
nlevel)
ph3 = Phonon.simple_phonon(Quantity(-omega), Quantity(-D * np.sinh(theta)),
nlevel)
mol2 = Mol(Quantity(0), [ph2, ph3])
mlist2 = MolList([mol2] * 2, Quantity(1), scheme=4)
mps1 = Mps.gs(mlist2, False)
mps1.evolve_config = evolve_config
mpo2 = Mpo(mlist2)
e2 = mps1.expectation(mpo2)
mps2 = (Mpo.onsite(mlist2, r"a^\dagger", False, {0})
@ mps1).expand_bond_dimension(mpo2)
es2 = [mps2.e_occupations]
for i in range(20):
mps2 = mps2.evolve(mpo2, 0.2)
es2.append(mps2.e_occupations)
assert np.allclose(es1[::2], es2, atol=5e-3)
def test_mpdm_full(nmols, phonon_freq):
ph = Phonon.simple_phonon(Quantity(phonon_freq), Quantity(1), 2)
m = Mol(Quantity(0), [ph])
mol_list = MolList([m] * nmols, Quantity(1))
gs_dm = MpDm.max_entangled_gs(mol_list)
beta = Quantity(1000, "K").to_beta()
tp = ThermalProp(gs_dm, Mpo(mol_list), exact=True, space="GS")
tp.evolve(None, 50, beta / 1j)
gs_dm = tp.latest_mps
assert np.allclose(gs_dm.e_occupations, [0] * nmols)
e_gs_dm = Mpo.onsite(mol_list, r"a^\dagger",
mol_idx_set={0}).apply(gs_dm, canonicalise=True)
assert np.allclose(e_gs_dm.e_occupations, [1] + [0] * (nmols - 1))
mpdm_full = MpDmFull.from_mpdm(e_gs_dm)
assert np.allclose(mpdm_full.e_occupations, e_gs_dm.e_occupations)
assert np.allclose(mpdm_full.ph_occupations,
e_gs_dm.ph_occupations,
rtol=1e-3)
def test_2site():
ph = Phonon.simple_phonon(Quantity(1), Quantity(1), 2)
m = Mol(Quantity(0), [ph])
mol_list = MolList([m] * 2, Quantity(1), scheme=3)
gs_mp = Mpo.onsite(mol_list, opera=r"a^\dagger", mol_idx_set={0}).apply(Mps.gs(mol_list, max_entangled=False))
mpdm = MpDm.from_mps(gs_mp)
mpdm_full = MpDmFull.from_mpdm(mpdm)
mpdm_full.compress_config = CompressConfig(threshold=1e-4)
liouville = SuperLiouville(Mpo(mol_list), dissipation=1)
ph_occupations_array = []
energies = []
for i in range(51):
logger.info(mpdm_full)
logger.info(mpdm_full.ph_occupations)
ph_occupations_array.append(mpdm_full.ph_occupations)
logger.info(mpdm_full.expectation(liouville))
energies.append(mpdm_full.expectation(liouville))
mpdm_full = mpdm_full.evolve(liouville, 0.4)
ph_occupations_array = np.array(ph_occupations_array)
assert energies[-1] == pytest.approx(-0.340162, rel=1e-2)
assert np.allclose(ph_occupations_array[-1], [0.0930588, 0.099115], rtol=1e-2)
def test_thermal_prop(mol_list, etot_std, occ_std, nsteps, evolve_method,
use_rk, rtol):
init_mps = MpDm.max_entangled_ex(mol_list)
mpo = Mpo(mol_list)
beta = Quantity(298, "K").to_beta()
evolve_time = beta / 2j
if nsteps is None:
evolve_config = EvolveConfig(evolve_method,
adaptive=True,
evolve_dt=beta / 100j)
else:
evolve_config = EvolveConfig(evolve_method)
if evolve_method is EvolveMethod.tdvp_ps:
evolve_config.tdvp_ps_rk4 = use_rk
tp = ThermalProp(init_mps, mpo, evolve_config=evolve_config)
tp.evolve(nsteps=nsteps, evolve_time=evolve_time)
mps = tp.latest_mps
MPO, HAM, Etot, A_el = mps.construct_hybrid_Ham(mpo, debug=True)
assert np.allclose(Etot, etot_std, rtol=rtol)
assert np.allclose(A_el, occ_std, rtol=rtol)
def test_ft():
model = get_model()
mpo = Mpo(model)
impdm = MpDm.max_entangled_gs(model)
impdm.compress_config = CompressConfig(threshold=1e-6)
temperature = Quantity(3)
evolve_config = EvolveConfig(adaptive=True, guess_dt=-0.001j)
tp = ThermalProp(impdm, mpo, evolve_config=evolve_config)
tp.evolve(nsteps=1, evolve_time=temperature.to_beta() / 2j)
mpdm = tp.latest_mps
mpdm = Mpo(model, Op("sigma_x", "spin")).contract(mpdm)
mpdm.evolve_config = EvolveConfig(adaptive=True, guess_dt=0.1)
time_series = [0]
sigma_z_oper = Mpo(model, Op("sigma_z", "spin"))
spin = [mpdm.expectation(sigma_z_oper)]
for i in range(29):
dt = mpdm.evolve_config.guess_dt
mpdm = mpdm.evolve(mpo, evolve_dt=dt)
time_series.append(time_series[-1] + dt)
spin.append(mpdm.expectation(sigma_z_oper))
qutip_res = get_qutip_ft(model, temperature, time_series)
assert np.allclose(qutip_res, spin, atol=1e-3)
def test_ft():
mol = get_mol()
mol_list = MolList([mol], Quantity(0))
mpo = Mpo(mol_list)
impdm = MpDm.max_entangled_gs(mol_list)
impdm.compress_config = CompressConfig(threshold=1e-6)
impdm.use_dummy_qn = True
temperature = Quantity(3)
evolve_config = EvolveConfig(adaptive=True, guess_dt=-0.001j)
tp = ThermalProp(impdm, mpo, evolve_config=evolve_config)
tp.evolve(nsteps=1, evolve_time=temperature.to_beta() / 2j)
mpdm = tp.latest_mps
mpdm = Mpo.onsite(mol_list, r"sigma_x").contract(mpdm)
mpdm.evolve_config = EvolveConfig(adaptive=True, guess_dt=0.1)
time_series = [0]
spin = [1 - 2 * mpdm.e_occupations[0]]
for i in range(30):
dt = mpdm.evolve_config.guess_dt
mpdm = mpdm.evolve(mpo, evolve_dt=dt)
time_series.append(time_series[-1] + dt)
spin.append(1 - 2 * mpdm.e_occupations[0])
exact = get_exact_ft(mol, temperature, time_series)
assert np.allclose(exact, spin, atol=1e-3)
