def test_spinmodel(tolerance=None):
from pyvmc.library.dmetal import DMetalWavefunction
wf = DMetalWavefunction(**{
'lattice': Lattice([12, 2]),
'd1': Bands([5, 3], (periodic, periodic)),
'd2': Bands([8, 0], (antiperiodic, periodic)),
'f_up': Bands([4, 0], (antiperiodic, periodic)),
'f_dn': Bands([4, 0], (antiperiodic, periodic)),
'd1_exponent': 0.7,
'd2_exponent': -0.4,
})
from pyvmc.operators import SpinModelRingExchangeOperator
from pyvmc.measurements import BasicOperatorMeasurementPlan
from pyvmc.core import LatticeSite
from pyvmc.core.universe import SimulationUniverse
spin_operator = SpinModelRingExchangeOperator(LatticeSite([0, 0]), LatticeSite([1, 0]),
LatticeSite([1, 1]), LatticeSite([0, 1]),
(periodic, periodic))
plans = [BasicOperatorMeasurementPlan(wf, o) for o in spin_operator.get_basic_operators()]
universe = SimulationUniverse(plans, equilibrium_sweeps=500000)
universe.iterate(1000000)
context = {mp.operator: m.get_estimate().result for mp, m in universe.get_overall_measurement_dict().items()}
logger.info("Spin model: %f", spin_operator.evaluate(context)())
def test_ansatz(lattice, t1, delta1, mu0, expected_results, tolerance):
parton_boundary_conditions = (periodic, antiperiodic)
from pyvmc.library.mft_utils import did_hf_bcs_theory
phi = did_hf_bcs_theory(lattice, parton_boundary_conditions, t1=t1, delta1=delta1, mu0=mu0, delta0=0)['pairing_matrix']
from pyvmc.library.bcs import ProjectedBCSWavefunction
wf = ProjectedBCSWavefunction(**{
'lattice': lattice,
'phi': phi,
'N_up': len(lattice) // 2,
})
from pyvmc.library.heisenberg_ring import HeisenbergPlusRingExchangeHamiltonian
from pyvmc.measurements import BasicOperatorMeasurementPlan
from pyvmc.core import LatticeSite
from pyvmc.core.universe import SimulationUniverse
hamiltonian = HeisenbergPlusRingExchangeHamiltonian(parton_boundary_conditions, lattice)
plans = [BasicOperatorMeasurementPlan(wf, o, steps_per_measurement=100) for o in hamiltonian.get_basic_operators()]
universe = SimulationUniverse(plans, equilibrium_sweeps=100000)
universe.iterate(1000000)
context = {mp.operator: m.get_estimate().result for mp, m in universe.get_overall_measurement_dict().items()}
evaluator = hamiltonian.evaluate(context)
final_results = (
evaluator(J1=1, J2=0, J3=0, K=0) / len(lattice) / 3,
evaluator(J1=0, J2=1, J3=0, K=0) / len(lattice) / 3,
evaluator(J1=0, J2=0, J3=1, K=0) / len(lattice) / 3,
evaluator(J1=0, J2=0, J3=0, K=1) / len(lattice) / 3,
)
logger.info("t1=%f, delta1=%f, mu0=%f", t1, delta1, mu0)
logger.info(" nn: %f", final_results[0])
logger.info(" 2nn: %f", final_results[1])
logger.info(" 3nn: %f", final_results[2])
logger.info("ring: %f", final_results[3])
assert all(abs(r1 - r2) < tolerance for r1, r2 in zip(final_results, expected_results))
def test_1d_free_fermion_renyi(tolerance=0.02):
N = 10
F = 5
lattice = Lattice([N])
orbitals = Bands([F], [periodic])
if False:
# a constant Jastrow factor shouldn't change anything
from pyvmc.core.wavefunction import TwoBodyJastrowFactor
jastrow_mat = numpy.empty((N, N))
jastrow_mat.fill(1)
jastrow = TwoBodyJastrowFactor(jastrow_mat)
else:
jastrow = None
wf = FreeFermionWavefunction(lattice=lattice, orbitals=[orbitals], jastrow=jastrow)
exact_values = [
free_fermions.exact_renyi(SimpleSubsystem([i], lattice), orbitals, [periodic], 2) for i in range(1, N // 2 + 1)
]
plans = [RenyiEntropyMeasurementPlan(wf, SimpleSubsystem([i], lattice)) for i in range(1, N // 2 + 1)]
calc = SimulationUniverse(plans, 500000)
while True:
calc.iterate(200000)
results = calc.get_overall_measurement_dict()
measured_values = [plan.calculate(lambda p, k=None: results[p].get_estimate(k).result) for plan in plans]
differences = [
measured_value - exact_value for measured_value, exact_value in zip(measured_values, exact_values)
]
logger.info("differences from expected: %s", differences)
if all(numpy.abs(d) < tolerance for d in differences):
break
# test hdf5
import h5py
filename = "/tmp/hdf5test_renyi.hdf5"
with h5py.File(filename, "w") as f:
calc.to_hdf5(f)
with h5py.File(filename, "r") as f:
universe2 = SimulationUniverse.from_hdf5(f, wf)
results2 = universe2.get_overall_measurement_dict()
measured_values2 = [plan.calculate(lambda p, k=None: results2[p].get_estimate(k).result) for plan in plans]
assert all(
numpy.abs(measured_value - exact_value) < tolerance
for measured_value, exact_value in zip(measured_values, exact_values)
)
def test_dmetal_energy(tolerance=None):
wf = DMetalWavefunction(**{
'lattice': Lattice([12, 2]),
'd1': Bands([5, 3], (periodic, periodic)),
'd2': Bands([8, 0], (antiperiodic, periodic)),
'f_up': Bands([4, 0], (antiperiodic, periodic)),
'f_dn': Bands([4, 0], (antiperiodic, periodic)),
'd1_exponent': 0.7,
'd2_exponent': -0.4,
})
from pyvmc.operators import TJKHamiltonian
from pyvmc.measurements import BasicOperatorMeasurementPlan
from pyvmc.core.universe import SimulationUniverse
hamiltonian = TJKHamiltonian((periodic, periodic), wf.lattice)
plans = [BasicOperatorMeasurementPlan(wf, o) for o in hamiltonian.get_basic_operators()]
universe = SimulationUniverse(plans, equilibrium_sweeps=500000)
universe.iterate(1000000)
context = {mp.operator: m.get_estimate().result for mp, m in universe.get_overall_measurement_dict().items()}
energy = hamiltonian.evaluate(context)(t=1, J=2, K=2) / len(wf.lattice)
logger.info("Energy: %f", energy)
assert -0.8 < energy < -0.74
# test hdf5
import h5py
filename = '/tmp/hdf5test_dmetal.hdf5'
with h5py.File(filename, 'w') as f:
grp = f.create_group('testgroup')
universe.to_hdf5(grp)
with h5py.File(filename, 'r') as f:
universe2 = SimulationUniverse.from_hdf5(f['testgroup'], wf)
context2 = {mp.operator: m.get_estimate().result for mp, m in universe2.get_overall_measurement_dict().items()}
energy = hamiltonian.evaluate(context)(t=1, J=2, K=2) / len(wf.lattice)
logger.info("Energy: %f", energy)
assert -0.8 < energy < -0.74