def test_ground_state(self):
length, n, h, U, t = 2, 0.8, 3.8, -6, 1
fu = generate_operators('fu', length)
fd = generate_operators('fd', length)
_b = flatten([fu, fd])
monomials = [[ci for ci in _b]]
monomials[-1].extend([Dagger(ci) for ci in _b])
monomials.append([cj*ci for ci in _b for cj in _b])
monomials.append([Dagger(cj)*ci for ci in _b for cj in _b])
monomials[-1].extend([cj*Dagger(ci)
for ci in _b for cj in _b])
monomials.append([Dagger(cj)*Dagger(ci)
for ci in _b for cj in _b])
hamiltonian = 0
for j in range(length):
hamiltonian += U * (Dagger(fu[j])*Dagger(fd[j]) * fd[j]*fu[j])
hamiltonian += -h/2*(Dagger(fu[j])*fu[j] - Dagger(fd[j])*fd[j])
for k in get_neighbors(j, len(fu), width=1):
hamiltonian += -t*Dagger(fu[j])*fu[k]-t*Dagger(fu[k])*fu[j]
hamiltonian += -t*Dagger(fd[j])*fd[k]-t*Dagger(fd[k])*fd[j]
momentequalities = [n-sum(Dagger(br)*br for br in _b)]
sdpRelaxation = SdpRelaxation(_b, verbose=0)
sdpRelaxation.get_relaxation(-1,
objective=hamiltonian,
momentequalities=momentequalities,
substitutions=fermionic_constraints(_b),
extramonomials=monomials)
sdpRelaxation.solve()
s = 0.5*(sum((Dagger(u)*u) for u in fu) -
sum((Dagger(d)*d) for d in fd))
magnetization = sdpRelaxation[s]
self.assertTrue(abs(magnetization-0.021325317328560453) < 10e-5)
def test_ground_state(self):
length, n, h, U, t = 2, 0.8, 3.8, -6, 1
fu = generate_operators('fu', length)
fd = generate_operators('fd', length)
_b = flatten([fu, fd])
monomials = [[ci for ci in _b]]
monomials[-1].extend([Dagger(ci) for ci in _b])
monomials.append([cj * ci for ci in _b for cj in _b])
monomials.append([Dagger(cj) * ci for ci in _b for cj in _b])
monomials[-1].extend([cj * Dagger(ci) for ci in _b for cj in _b])
monomials.append([Dagger(cj) * Dagger(ci) for ci in _b for cj in _b])
hamiltonian = 0
for j in range(length):
hamiltonian += U * (Dagger(fu[j]) * Dagger(fd[j]) * fd[j] * fu[j])
hamiltonian += -h / 2 * (Dagger(fu[j]) * fu[j] -
Dagger(fd[j]) * fd[j])
for k in get_neighbors(j, len(fu), width=1):
hamiltonian += -t * Dagger(fu[j]) * fu[k] - t * Dagger(
fu[k]) * fu[j]
hamiltonian += -t * Dagger(fd[j]) * fd[k] - t * Dagger(
fd[k]) * fd[j]
momentequalities = [n - sum(Dagger(br) * br for br in _b)]
sdpRelaxation = SdpRelaxation(_b, verbose=0)
sdpRelaxation.get_relaxation(-1,
objective=hamiltonian,
momentequalities=momentequalities,
substitutions=fermionic_constraints(_b),
extramonomials=monomials)
sdpRelaxation.solve()
s = 0.5 * (sum((Dagger(u) * u) for u in fu) - sum(
(Dagger(d) * d) for d in fd))
magnetization = sdpRelaxation[s]
self.assertTrue(abs(magnetization - 0.021325317328560453) < 10e-5)
def test_apply_substitutions(self):
def apply_correct_substitutions(monomial, substitutions):
if isinstance(monomial, int) or isinstance(monomial, float):
return monomial
original_monomial = monomial
changed = True
while changed:
for lhs, rhs in substitutions.items():
monomial = monomial.subs(lhs, rhs)
if original_monomial == monomial:
changed = False
original_monomial = monomial
return monomial
length, h, U, t = 2, 3.8, -6, 1
fu = generate_operators('fu', length)
fd = generate_operators('fd', length)
_b = flatten([fu, fd])
hamiltonian = 0
for j in range(length):
hamiltonian += U * (Dagger(fu[j])*Dagger(fd[j]) * fd[j]*fu[j])
hamiltonian += -h/2*(Dagger(fu[j])*fu[j] - Dagger(fd[j])*fd[j])
for k in get_neighbors(j, len(fu), width=1):
hamiltonian += -t*Dagger(fu[j])*fu[k]-t*Dagger(fu[k])*fu[j]
hamiltonian += -t*Dagger(fd[j])*fd[k]-t*Dagger(fd[k])*fd[j]
substitutions = fermionic_constraints(_b)
monomials = expand(hamiltonian).as_coeff_mul()[1][0].as_coeff_add()[1]
substituted_hamiltonian = sum([apply_substitutions(monomial,
substitutions)
for monomial in monomials])
correct_hamiltonian = sum([apply_correct_substitutions(monomial,
substitutions)
for monomial in monomials])
self.assertTrue(substituted_hamiltonian == expand(correct_hamiltonian))
def test_apply_substitutions(self):
def apply_correct_substitutions(monomial, substitutions):
if isinstance(monomial, int) or isinstance(monomial, float):
return monomial
original_monomial = monomial
changed = True
while changed:
for lhs, rhs in substitutions.items():
monomial = monomial.subs(lhs, rhs)
if original_monomial == monomial:
changed = False
original_monomial = monomial
return monomial
length, h, U, t = 2, 3.8, -6, 1
fu = generate_operators('fu', length)
fd = generate_operators('fd', length)
_b = flatten([fu, fd])
hamiltonian = 0
for j in range(length):
hamiltonian += U * (Dagger(fu[j])*Dagger(fd[j]) * fd[j]*fu[j])
hamiltonian += -h/2*(Dagger(fu[j])*fu[j] - Dagger(fd[j])*fd[j])
for k in get_neighbors(j, len(fu), width=1):
hamiltonian += -t*Dagger(fu[j])*fu[k]-t*Dagger(fu[k])*fu[j]
hamiltonian += -t*Dagger(fd[j])*fd[k]-t*Dagger(fd[k])*fd[j]
substitutions = fermionic_constraints(_b)
monomials = expand(hamiltonian).as_coeff_mul()[1][0].as_coeff_add()[1]
substituted_hamiltonian = sum([apply_substitutions(monomial,
substitutions)
for monomial in monomials])
correct_hamiltonian = sum([apply_correct_substitutions(monomial,
substitutions)
for monomial in monomials])
self.assertTrue(substituted_hamiltonian == expand(correct_hamiltonian))
def createSubstitutions(self):
return fermionic_constraints(self._b)
