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)
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
print