def runSpectrumComparisonWithSasha(self):
mu = 0.27
beta = 20
results = list()
u = 3
t = -1
r = 0.3
h = Hubbard([[-mu, t, t, r], [t, -mu, r, t], [t, r, -mu, t], [r, t, t, -mu]], u, verbose=False)
h.solve()
energies = list(h.eigenEnergies)
energiesSasha = numpy.loadtxt("spectrumSasha.dat")[:, 1]
self.assertEqual(len(energies), len(energiesSasha))
for j, eS in enumerate(energiesSasha):
energyFound = False
for i, e in enumerate(energies):
if equals(eS, e):
energyFound = True
del energies[i]
break
self.assertTrue(energyFound)
def runEigenstatesEquation(self):
mu = 0.27
beta = 20
results = list()
u = 3
t = -1
r = 0.3
h = Hubbard([[-mu, t, t, r], [t, -mu, r, t], [t, r, -mu, t], [r, t, t, -mu]], u, verbose=False)
h.solve()
hmatrix = h.matrix
statesMatrix = h.eigenStates.toarray()
for i in range(256):
e = h.eigenEnergies[i] + h.energyShift
ve = statesMatrix[:, i]
eve = hmatrix.dot(ve)
zeros = eve - e * ve
for zero in zeros:
self.assertTrue(
equals(zero, 0, rtol=1e-05, atol=1e-12)
) # max abs tolerance with scipy.linalg.eigh for that system
def runHubbardAtom(self):
h = Hubbard([[-0.5]], 1)
h.solve()
self.assertEqual(-0.5, h.getGroundStateEnergy())
self.assertEqual(h.getEnergies(), [0, 0.5])
self.assertTrue((h.eigenEnergies == numpy.array([0.5, 0, 0, 0.5])).all())
for state in h.getGroundStatesAlgebraically():
self.assertTrue(state in ["+1.0 c^('up', 0)\n", "+1.0 c^('dn', 0)\n"])
for states_e, e in zip(h.getStatesEnergySortedAlgebraically(), h.getEnergies()):
for state in states_e:
if e == 0:
self.assertTrue(state in ["+1.0 c^('up', 0)\n", "+1.0 c^('dn', 0)\n"])
elif e == 0.5:
self.assertTrue(state in ["+1.0 \n", "+1.0 c^('up', 0) c^('dn', 0)\n"])
else:
self.assertTrue(False)
c = AnnihilationOperator(h.getSingleParticleBasis())
n_tot_hat = numpy.sum([c[s, 0].H.dot(c[s, 0]) for s in ["up", "dn"]], axis=0)
self.assertEqual(h.getGroundStates()[0].getQuantumNumber(n_tot_hat), 1)
self.assertEqual(h.getGroundStates()[1].getQuantumNumber(n_tot_hat), 1)
u = 3 mu = u*.5 hop = [[0,t,t,tp],[t,0,tp,t],[t,tp,0,t],[tp,t,t,0]] hamiltonian = Hubbard2(hop, u) plaq = GrandcanonicalEnsemble(hamiltonian, beta, mu) plaq.calcEigensystem() e0 = plaq.hamiltonian.getGroundStateEnergy() energies = plaq.hamiltonian.eigenEnergies eigenstates = plaq.hamiltonian.eigenStates.toarray() rho_dim = RDM(beta, eigenstates, energies, 4, 4, [], [0]) rho_dim.calculate() print rho_dim.get_entanglement_spectrum() print rho_dim.get_entanglement_entropy() hamiltonian = Hubbard(hop, u) print hamiltonian.singleParticleBasis plaq = GrandcanonicalEnsemble(hamiltonian, beta, mu) plaq.calcEigensystem() e0 = plaq.hamiltonian.getGroundStateEnergy() energies = plaq.hamiltonian.eigenEnergies eigenstates = plaq.hamiltonian.eigenStates.toarray() rho_0 = RDM(beta, eigenstates, energies, 4, 4, [(3,4),(2,3),(1,2),(4,5),(3,4)], [0]) rho_0.calculate() print rho_0.get_entanglement_spectrum() print rho_0.get_entanglement_entropy() hamiltonian = Hubbard(hop, u) plaq = GrandcanonicalEnsemble(hamiltonian, beta, mu) plaq.calcEigensystem() e0 = plaq.hamiltonian.getGroundStateEnergy()
with h5py.File('intersectionstprime.h5', 'r') as data:
i_tnnn = np.where(data['tnnns'][:] == tnnn)[0]
phaseboundary = data['intersections'][i_tnnn, 1]
return phaseboundary
beta = 30
t = -1
tp = .3
hop = [[0, t, t, tp], [t, 0, tp, t], [t, tp, 0, t], [tp, t, t, 0]]
umu = get_u_mu24(0.3)
results = []
for u, mu in zip(umu[0, :, 0], umu[0, :, 1]):
print u, mu
hamiltonian = Hubbard(hop, u) # basis: [['up', 'dn'], [0, 1, 2, 3]]
plaq = GrandcanonicalEnsemble(hamiltonian, beta, mu)
plaq.calcEigensystem()
energies = plaq.hamiltonian.eigenEnergies
eigenstates = plaq.hamiltonian.eigenStates.toarray()
rho_0 = RDM(beta, eigenstates, energies, 2, 6, [(3, 4), (2, 3), (1, 2)],
range(9))
rho_0.calculate()
rho_01 = RDM(beta, eigenstates, energies, 4, 4, [(3, 4), (2, 3), (1, 2),
(4, 5), (3, 4)], range(9))
rho_01.calculate()
rho_03 = RDM(beta, eigenstates, energies, 4, 4, [(3, 4), (2, 3), (1, 2),
(3, 4), (2, 3), (6, 7),
(5, 6), (4, 5), (3, 4)],
range(9))
rho_03.calculate()
from EasyED.hamiltonians import Hubbard
from EasyED.operators import AnnihilationOperator
from EasyED.util import report
from itertools import product
from matplotlib import pyplot as plt
from numpy import array, sqrt, sort, arange
import numpy
numpy.set_printoptions(suppress=True)
structure = Hubbard([[.5, 0], [0, .5]], 1)
c = AnnihilationOperator(structure.getSingleParticleBasis())
report(structure.blocksizes)
structure.solve()
print structure.eigenEnergies
print 'groundstateenergy: ', structure.getGroundStateEnergy()
print 'groundstates:'
for state in structure.getGroundStatesAlgebraically():
print state
print
print 'states:'
for energyGroup, energy in zip(structure.getStatesEnergySortedAlgebraically(), structure.getEnergies()):
print 'E = ', energy
print
for state in energyGroup:
print state
