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)
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
print
sz_tot = .5 * (c['up', 0].H.dot(c['up', 0]) - c['dn', 0].H.dot(c['dn', 0])) + .5 * (c['up', 1].H.dot(c['up', 1]) - c['dn', 1].H.dot(c['dn', 1]))
chi_zz_tot = sz_tot.dot(sz_tot)
print 'corresponding S2_tot qnrs:'
energies, degeneracies = structure.getSpectrum()
for energyGroup, energy in zip(structure.getSuperpositionStatesEnergySorted(), sort(energies)):
for state in energyGroup:
print str(energy)+' -> '+str(3*state.getQuantumNumber(chi_zz_tot))
print