def get_propagator(beta, mpa_type, system_index, h_site, h_bond, rank=1, state_compression_kwargs=None,
op_compression_kwargs=None, psi_0_compression_kwargs=None, second_order_trotter=False,
seed=102):
"""
Returns the propagator object for imaginary time evolution ground state generation
:param beta: Decay coefficient
:param mpa_type: Type of mpa to evolve (allowed are 'mps', 'pmps' and 'mpo')
:param system_index: Index of the system site in the chain (place of the system site operator in h_site)
:param h_site: local operators of hamiltonian as list or tuple
:param h_bond: iterator over bond (coupling) operators of the Hamiltonian
:param rank: Rank of the random initial state (default is 1)
:param state_compression_kwargs: Arguments for mps compression after each second order trotter step U(tau_i).
(see real time evolution factory function for details)
:param op_compression_kwargs: Arguments for trotter step operator precompression (see real time evolution
factory function for details)
:param second_order_trotter: Uses second order trotter steps for the propagation
:param seed: Seed for the initial random state
:param psi_0_compression_kwargs: Optional compression kwargs for the initial state (see real time evolution
factory function for details)
"""
tau = -beta
axis_0 = []
for index, site in enumerate(h_site):
assert site.shape[0] == site.shape[1]
axis_0.append(site.shape[0])
psi_0 = get_random_mpa(mpa_type, axis_0, seed=seed, rank=rank)
return propagator_from_hamiltonian(psi_0, mpa_type, system_index, h_site, h_bond, tau=tau,
state_compression_kwargs=state_compression_kwargs,
op_compression_kwargs=op_compression_kwargs,
psi_0_compression_kwargs=psi_0_compression_kwargs,
second_order_trotter=second_order_trotter, t0=0,
track_trace=False)
def get_propagator_from_hi(beta, mpa_type, system_index, dims, hi_list, rank=1, state_compression_kwargs=None,
op_compression_kwargs=None, second_order_trotter=False, seed=102,
psi_0_compression_kwargs=None):
"""
Returns the propagator object for imaginary time evolution ground state generation
:param beta: Decay coefficient
:param mpa_type: Type of mpa to evolve (allowed are 'mps', 'pmps' and 'mpo')
:param system_index: Index of the system site in the chain (place of the system site operator in the hi_list)
:param dims: Physical dimensions in the chain
:param hi_list: List/Tuple of all terms in the Hamiltonian H = sum_i hi, where hi is local to one bond
:param rank: Rank of the random initial state (default is 1)
:param state_compression_kwargs: Arguments for mps compression after each second order trotter step U(tau_i).
(see real time evolution factory function for details)
:param op_compression_kwargs: Arguments for trotter step operator precompression (see real time evolution
factory function for details)
:param second_order_trotter: Uses second order trotter steps for the propagation
:param seed: Seed for the initial random state
:param psi_0_compression_kwargs: Optional compression kwargs for the initial state (see real time evolution
factory function for details)
"""
tau = -beta
psi_0 = get_random_mpa(mpa_type, dims, seed=seed, rank=rank)
return propagator_from_hi(psi_0, mpa_type, system_index, hi_list, tau=tau,
state_compression_kwargs=state_compression_kwargs,
op_compression_kwargs=op_compression_kwargs,
psi_0_compression_kwargs=psi_0_compression_kwargs,
second_order_trotter=second_order_trotter, t0=0,
track_trace=False)
def test_regular_chain_random(L, sot, nof_steps, tau):
"""
Pytest test for time evolution of a pure quantum state in mps form under a Hamiltonian of the form:
sum_i^L H_{i} + sum_i^(L-1) H_{i, i+1}
where the H_(i) are called site ops and the H_{i, i+1} are called bond ops, both are randomized.
The physical dimension of each site (site_dim) is constant d!
Tests are performed for different chain lengths and different time discretizations.
The initial state is randomized.
:param L: Chain L
:param nof_steps: Number of time evolution steps
:param tau: Timestep in each step of the time evolution
:return:
"""
# Parameters
site_dim = 2
site_dims = [site_dim] * L
mps_psi_0 = get_random_mpa('mps', site_dims, rank=2, seed=103)
psi_0 = mp.MPArray.to_array(mps_psi_0).reshape(site_dim**L)
site_op = pauli.Z
bond_op = np.kron(pauli.Z, pauli.X)
# Setup for exact diagonalization
exdiag_propagator = exdiag.ExDiagPropagator(psi_0, site_dims,
repeat(site_op, L),
repeat(bond_op, L - 1), tau)
# Setup for tMPS evolution
state_compress_kwargs = {'method': 'svd', 'relerr': 1e-10}
op_compression_kwargs = {'method': 'svd', 'relerr': 1e-13}
tmps_propagator = from_hamiltonian(
mps_psi_0,
'mps',
site_op,
bond_op,
tau=tau,
state_compression_kwargs=state_compress_kwargs,
op_compression_kwargs=op_compression_kwargs,
second_order_trotter=sot)
normdist = []
itno = 0
for step in range(nof_steps):
exdiag_propagator.evolve()
tmps_propagator.fast_evolve()
tmps_psi_t_array = mp.MPArray.to_array(tmps_propagator.psi_t).reshape(
site_dim**L)
normdist.append(
np.linalg.norm(tmps_psi_t_array - exdiag_propagator.psi_t))
itno += 1
max_normdist = np.max(np.array(normdist))
if sot:
assert np.max(max_normdist) < 1e-6
else:
assert np.max(max_normdist) < 1e-8