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 get_mol():
nphonons = 5
ph_levels = 2
delta = 1
epsilon = 1
ph_list = [Phonon.simple_phonon(Quantity(1), Quantity(1), ph_levels)
] * nphonons
m = Mol(Quantity(epsilon), ph_list, tunnel=Quantity(-delta))
return m
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 test_offset(scheme):
ph = Phonon.simple_phonon(Quantity(3.33), Quantity(1), 2)
m = Mol(Quantity(0), [ph] * 2)
mlist = MolList([m] * 2, Quantity(17), scheme=scheme)
mpo1 = Mpo(mlist)
assert mpo1.is_hermitian()
f1 = mpo1.full_operator()
evals1, _ = np.linalg.eigh(f1.asnumpy())
offset = Quantity(0.123)
mpo2 = Mpo(mlist, offset=offset)
f2 = mpo2.full_operator()
evals2, _ = np.linalg.eigh(f2.asnumpy())
assert np.allclose(evals1 - offset.as_au(), evals2)
def test_band_limit_finite_t(mol_num, j_constant_value, elocalex_value,
ph_info, ph_phys_dim, evolve_dt, nsteps, scheme):
ph_list = [
Phonon.simple_phonon(Quantity(omega, "cm^{-1}"),
Quantity(displacement, "a.u."), ph_phys_dim)
for omega, displacement in ph_info
]
mol_list = MolList([Mol(Quantity(elocalex_value, "a.u."), ph_list)] *
mol_num,
Quantity(j_constant_value, "eV"),
scheme=scheme)
ct1 = ChargeTransport(mol_list, stop_at_edge=False)
ct1.evolve(evolve_dt, nsteps)
ct2 = ChargeTransport(mol_list, temperature=low_t, stop_at_edge=False)
ct2.evolve(evolve_dt, nsteps)
assert ct1.is_similar(ct2)
def test_similar(mol_num, j_constant_value, elocalex_value, ph_info,
ph_phys_dim, evolve_dt, nsteps):
ph_list = [
Phonon.simple_phonon(Quantity(omega, "cm^{-1}"),
Quantity(displacement, "a.u."), ph_phys_dim)
for omega, displacement in ph_info
]
mol_list = MolList([Mol(Quantity(elocalex_value, "a.u."), ph_list)] *
mol_num,
Quantity(j_constant_value, "eV"),
scheme=3)
ct1 = ChargeTransport(mol_list)
ct1.evolve(evolve_dt, nsteps)
ct2 = ChargeTransport(mol_list)
ct2.evolve(evolve_dt + 1e-5, nsteps)
assert ct1.is_similar(ct2)
def test_autocorr(insteps, atol):
ph = Phonon.simple_phonon(Quantity(1), Quantity(1), 2)
mol = Mol(Quantity(0), [ph])
mol_list = MolList([mol] * 5, Quantity(1), 3)
temperature = Quantity(50000, 'K')
compress_config = CompressConfig(threshold=1e-3)
ac = TransportAutoCorr(mol_list,
temperature,
insteps,
compress_config=compress_config)
ac.evolve(0.2, 50)
corr_real = ac.auto_corr.real
exact_real = get_exact_autocorr(mol_list, temperature,
ac.evolve_times_array).real
# direct comparison may fail because of different sign
assert np.allclose(corr_real, exact_real, atol=atol) or np.allclose(
corr_real, -exact_real, atol=atol)
def test_scheme4_finite_t(mol_num, j_constant_value, elocalex_value, ph_info,
ph_phys_dim, evolve_dt, nsteps):
temperature = Quantity(1, "a.u.")
ph_list = [
Phonon.simple_phonon(Quantity(omega, "cm^{-1}"),
Quantity(displacement, "a.u."), ph_phys_dim)
for omega, displacement in ph_info
]
mol_list = MolList([Mol(Quantity(elocalex_value, "a.u."), ph_list)] *
mol_num, Quantity(j_constant_value, "eV"))
ct1 = ChargeTransport(mol_list.switch_scheme(3),
temperature=temperature,
stop_at_edge=False)
ct1.evolve(evolve_dt, nsteps)
ct2 = ChargeTransport(mol_list.switch_scheme(4),
temperature=temperature,
stop_at_edge=False)
ct2.evolve(evolve_dt, nsteps)
assert ct1.is_similar(ct2, rtol=1e-2)
def test_compress_add(mol_num, j_constant_value, elocalex_value, ph_info,
ph_phys_dim, evolve_dt, nsteps):
ph_list = [
Phonon.simple_phonon(Quantity(omega, "cm^{-1}"),
Quantity(displacement, "a.u."), ph_phys_dim)
for omega, displacement in ph_info
]
mol_list = MolList([Mol(Quantity(elocalex_value, "a.u."), ph_list)] *
mol_num,
Quantity(j_constant_value, "eV"),
scheme=3)
ct1 = ChargeTransport(mol_list, temperature=Quantity(298, "K"))
ct1.reduced_density_matrices = None
ct1.evolve(evolve_dt, nsteps)
ct2 = ChargeTransport(mol_list, temperature=Quantity(298, "K"))
ct2.reduced_density_matrices = None
ct2.latest_mps.compress_add = True
ct2.evolve(evolve_dt, nsteps)
assert ct1.is_similar(ct2, rtol=1e-2)
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_reduced_density_matrix(
mol_num,
j_constant_value,
elocalex_value,
ph_info,
ph_phys_dim,
evolve_dt,
nsteps,
temperature,
):
ph_list = [
Phonon.simple_phonon(Quantity(omega, "cm^{-1}"),
Quantity(displacement, "a.u."), ph_phys_dim)
for omega, displacement in ph_info
]
mol_list3 = MolList(
[Mol(Quantity(elocalex_value, "a.u."), ph_list)] * mol_num,
Quantity(j_constant_value, "eV"),
scheme=3,
)
ct3 = ChargeTransport(mol_list3,
temperature=Quantity(temperature, "K"),
stop_at_edge=False,
rdm=True)
ct3.evolve(evolve_dt, nsteps)
mol_list4 = mol_list3.switch_scheme(4)
ct4 = ChargeTransport(mol_list4,
temperature=Quantity(temperature, "K"),
stop_at_edge=False,
rdm=True)
ct4.evolve(evolve_dt, nsteps)
for rdm3, rdm4, e in zip(ct3.reduced_density_matrices,
ct4.reduced_density_matrices,
ct3.e_occupations_array):
assert np.allclose(rdm3, rdm4, atol=1e-3)
assert np.allclose(np.diag(rdm3), e)
def test_holstein_kubo(scheme):
ph = Phonon.simple_phonon(Quantity(1), Quantity(1), 2)
mol = Mol(Quantity(0), [ph])
model = HolsteinModel([mol] * 5, Quantity(1), scheme)
temperature = Quantity(50000, 'K')
compress_config = CompressConfig(CompressCriteria.fixed, max_bonddim=24)
evolve_config = EvolveConfig(EvolveMethod.tdvp_ps,
adaptive=True,
guess_dt=0.5,
adaptive_rtol=1e-3)
ievolve_config = EvolveConfig(EvolveMethod.tdvp_ps,
adaptive=True,
guess_dt=-0.1j)
kubo = TransportKubo(model,
temperature,
compress_config=compress_config,
ievolve_config=ievolve_config,
evolve_config=evolve_config)
kubo.evolve(nsteps=5, evolve_time=5)
qutip_res = get_qutip_holstein_kubo(model, temperature,
kubo.evolve_times_array)
rtol = 5e-2
assert np.allclose(kubo.auto_corr, qutip_res, rtol=rtol)
# -*- coding: utf-8 -*-
import numpy as np
from renormalizer.model import Phonon, Mol, HolsteinModel
from renormalizer.utils import Quantity
from renormalizer.transport import EDGE_THRESHOLD
mol_num = 13
ph_list = [
Phonon.simple_phonon(Quantity(omega, "cm^{-1}"), Quantity(displacement, "a.u."), 4)
for omega, displacement in [[1e-10, 1e-10]]
]
j_constant = Quantity(0.8, "eV")
band_limit_model = HolsteinModel([Mol(Quantity(0), ph_list)] * mol_num, j_constant, 3)
# the temperature should be compatible with the low vibration frequency in TestBandLimitFiniteT
# otherwise underflow happens in exact propagator
low_t = Quantity(1e-7, "K")
def get_analytical_r_square(time_series: np.ndarray):
return 2 * (j_constant.as_au()) ** 2 * time_series ** 2
def assert_band_limit(ct, rtol):
analytical_r_square = get_analytical_r_square(ct.evolve_times_array)
# has evolved to the edge but not too large
assert EDGE_THRESHOLD < ct.latest_mps.e_occupations[0] < 0.1
# value OK
assert np.allclose(analytical_r_square, ct.r_square_array, rtol=rtol)
# -*- coding: utf-8 -*- import numpy as np from renormalizer.mps import Mpo from renormalizer.model import Phonon, Mol, MolList from renormalizer.utils import Quantity from renormalizer.utils.qutip_utils import get_clist, get_blist, get_hamiltonian, get_gs OMEGA = 1 DISPLACEMENT = 1 N_LEVELS = 2 N_SITES = 3 J = 1 ph = Phonon.simple_phonon(Quantity(OMEGA), Quantity(DISPLACEMENT), N_LEVELS) mol = Mol(Quantity(0), [ph]) mol_list = MolList([mol] * N_SITES, Quantity(J), 3) qutip_clist = get_clist(N_SITES, N_LEVELS) qutip_blist = get_blist(N_SITES, N_LEVELS) G = np.sqrt(DISPLACEMENT**2 * OMEGA / 2) qutip_h = get_hamiltonian(N_SITES, J, OMEGA, G, qutip_clist, qutip_blist) qutip_gs = get_gs(N_SITES, N_LEVELS)