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_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 createHamiltonian(self):
if self._lattice_width != 1:
raise NotImplementedError("Higher dimension not implemented!")
if self._periodic or self._periodic == 1:
bext = self._b + [bi for bi in self._b]
elif self._periodic == -1:
bext = self._b + [-bi for bi in self._b]
else:
bext = self._b
hamiltonian = 0
for r, br in enumerate(self._b[:self._lattice_length]):
if self.mu != 0:
hamiltonian += -self.mu * (Dagger(br) * br - 1 / 2)
for s in get_neighbors(r, len(bext), self._lattice_width):
hamiltonian += -self.t * \
(Dagger(br) * bext[s] + Dagger(bext[s]) * br)
for d in range(1, self._lattice_length):
for s in get_next_neighbors(r, len(bext), self._lattice_width):
hamiltonian += self.Delta * \
math.pow(d, -self.alpha) * (br * bext[s] +
Dagger(bext[s]) * Dagger(br))
return hamiltonian
def createHamiltonian(self):
if self._periodic == -1:
raise NotImplementedError("Anti periodic not implemented!")
# fuext = self._fu + [-fi for fi in self._fu]
# fdext = self._fd + [-fi for fi in self._fd]
else:
fuext = self._fu
fdext = self._fd
hamiltonian = 0
V = self.getSize()
if self.t != 0:
for j in range(V):
for k in get_neighbors(j, self.getLength(),
width=self.getWidth(),
periodic=self._periodic):
hamiltonian += -self.t * Dagger(fuext[j]) * fuext[k]\
- self.t * Dagger(fuext[k]) * fuext[j]
hamiltonian += -self.t * Dagger(fdext[j]) * fdext[k]\
- self.t * Dagger(fdext[k]) * fdext[j]
if self.U != 0:
for j in range(V):
hamiltonian += self.U * (Dagger(fuext[j]) * Dagger(fdext[j]) *
fdext[j] * fuext[j])
if self.h != 0:
for j in range(V):
hamiltonian += -self.h / 2 * (Dagger(fuext[j]) * fuext[j] -
Dagger(fdext[j]) * fdext[j])
if self.mu != 0:
for j in range(V):
hamiltonian += -self.mu * (Dagger(fuext[j]) * fuext[j] +
Dagger(fdext[j]) * fdext[j])
return hamiltonian
def createHamiltonian(self):
if self._periodic == -1:
raise NotImplementedError("Antiperiodic boundary conditions not "
"implemented!")
hamiltonian = 0
for r, br in enumerate(self._b):
if self.U != 0:
hamiltonian += self.U / 2.0 * \
(Dagger(br) * br * (Dagger(br) * br - 1))
if self.mu != 0:
hamiltonian += -self.mu * Dagger(br) * br
if self.t != 0:
for s in get_neighbors(r, self._lattice_length,
self._lattice_width, self._periodic):
hamiltonian += -self.t * (Dagger(br) * self._b[s] +
Dagger(self._b[s]) * br)
if self.t2 != 0:
for s in get_next_neighbors(r, self._lattice_length,
self._lattice_width, 2,
self._periodic):
hamiltonian += -self.t2 * (Dagger(br) * self._b[s] +
Dagger(self._b[s]) * br)
return hamiltonian
