def calc_phase_diagram():
"""
Calculating the phase diagram of transverse field Ising model in $h$ and $J$ grid.
$h$ and $J$ both range from -100 to 100. The result is saved in an npz file.
:return: None.
"""
logspace = list(np.logspace(-2, 2, 20))
minus_logspace = list(-np.logspace(-2, 2, 20)[::-1])
j_grid = minus_logspace + [0] + logspace
h_grid = minus_logspace + [0] + logspace
mz_result = np.zeros((len(j_grid), len(h_grid)))
mx_result = np.zeros((len(j_grid), len(h_grid)))
for j_idx, j in enumerate(j_grid):
for h_idx, h in enumerate(h_grid):
param_str = "j = %g, h = %g" % (j, h)
logging.info("Start: " + param_str)
mpo_list = build_mpo_list(construct_single_mpo(j, h), SITE_NUM)
mps = MatrixProductState(mpo_list, error_threshold=ERROR_THRESHOLD)
energies = mps.search_ground_state()
mz = mps.expectation(construct_mz_mpo_list(SITE_NUM))
mx = mps.expectation(construct_mx_mpo_list(SITE_NUM))
mz_result[j_idx][h_idx] = mz
mx_result[j_idx][h_idx] = mx
logging.info("End %s. Energy: %g, M_z: %g, M_x: %g" %
(param_str, energies[-1], mz, mx))
np.savez(
"ising_phase_diagram",
mz_result=mz_result,
mx_result=mx_result,
j_grid=j_grid,
h_grid=h_grid,
)
def calc_mx_vs_h():
"""
Calculate the relation between $M_x$ and $h$ when $J$ is fixed to 1 and $h$ varies from 0 to 2
to study the phase transition. Energies are also calculated as a reference.
The result is saved in an npz file.
:return: None
"""
h_list = np.linspace(0, 2, 20)
energy_list = []
mx_list = []
for h in h_list:
logging.info("Start: h = %g" % h)
mpo_list = build_mpo_list(construct_single_mpo(j=1, h=h), SITE_NUM)
mps = MatrixProductState(mpo_list, error_threshold=ERROR_THRESHOLD)
energies = mps.search_ground_state()
mx = mps.expectation(construct_mx_mpo_list(SITE_NUM))
average_energy = energies[-1] / SITE_NUM
energy_list.append(average_energy)
mx_list.append(mx)
logging.info("End h = %g. Energy: %g, M_x: %g" %
(h, average_energy, mx))
np.savez("ising_mx_vs_h",
h_list=h_list,
energy_list=energy_list,
mx_list=mx_list)
def test_search():
mpo_list = build_mpo_list(construct_single_mpo(), SITE_NUM)
mps = MatrixProductState(mpo_list, max_bond_dimension=MAX_BOND_DIMENSION)
# use threshold as criterion for compression
# mps = MatrixProductState(mpo_list, error_threshold=ERROR_THRESHOLD)
energies = mps.search_ground_state()
assert pytest.approx(energies[-1], -10, abs=0.1)
def construct_mx_mpo_list(site_num):
"""
Construct the $M_x$ MPO list needed for calculating the expectation value of $M_x$ for a MPS
:param site_num: number of sites
:return: $M_x$ mpo list
"""
mpo_list = build_mpo_list(np.float64([[S1, S0], [Sx, S1]]),
site_num,
regularize=True)
return mpo_list
mpo_block3 = [Sm, S0, S0, S0, S0]
mpo_block4 = [Sz, S0, S0, S0, S0]
mpo_block5 = [-h * Sz, J / 2 * Sm, J / 2 * Sp, Jz * Sz, S1]
# MPO shape: 5, 5, 2, 2
mpo = np.float64(
[mpo_block1, mpo_block2, mpo_block3, mpo_block4, mpo_block5])
# prohibit writing just in case
mpo.flags.writeable = False
return mpo
# number of sites
SITE_NUM = 20
# only one of the following 2 parameters are needed
# maximum bond order in MPS
MAX_BOND_ORDER = 16
# the threshold for error when compressing MPS
ERROR_THRESHOLD = 1e-7
if __name__ == "__main__":
mpo_list = build_mpo_list(construct_single_mpo(), SITE_NUM)
mps = MatrixProductState(mpo_list, max_bond_order=MAX_BOND_ORDER)
# use threshold as criterion for compression
# mps = MatrixProductState(mpo_list, error_threshold=ERROR_THRESHOLD)
print(mps.search_ground_state())