def test_trimer_hamiltonian():
# ------------------------------------------------------------------
# -- Hubbard atom with two bath sites, Hamiltonian
beta = 2.0
V1 = 2.0
V2 = 5.0
epsilon1 = 0.00
epsilon2 = 4.00
mu = 2.0
U = 1.0
# -- construction using triqs operators
up, do = 0, 1
docc = c_dag(up,0) * c(up,0) * c_dag(do,0) * c(do,0)
nA = c_dag(up,0) * c(up,0) + c_dag(do,0) * c(do,0)
nB = c_dag(up,1) * c(up,1) + c_dag(do,1) * c(do,1)
nC = c_dag(up,2) * c(up,2) + c_dag(do,2) * c(do,2)
H_expr = -mu * nA + epsilon1 * nB + epsilon2 * nC + U * docc + \
V1 * (c_dag(up,0)*c(up,1) + c_dag(up,1)*c(up,0) + \
c_dag(do,0)*c(do,1) + c_dag(do,1)*c(do,0) ) + \
V2 * (c_dag(up,0)*c(up,2) + c_dag(up,2)*c(up,0) + \
c_dag(do,0)*c(do,2) + c_dag(do,2)*c(do,0) )
# ------------------------------------------------------------------
fundamental_operators = [
c(up,0), c(do,0), c(up,1), c(do,1), c(up,2), c(do,2)]
rep = SparseMatrixRepresentation(fundamental_operators)
H_mat = rep.sparse_matrix(H_expr)
# -- explicit construction
class Dummy(object):
def __init__(self):
pass
op = Dummy()
op.cdagger = rep.sparse_operators.c_dag
op.c = np.array([cdag.getH() for cdag in op.cdagger])
op.n = np.array([ cdag*cop for cop, cdag in zip(op.c, op.cdagger)])
H_ref = -mu * (op.n[0] + op.n[1]) + \
epsilon1 * (op.n[2] + op.n[3]) + \
epsilon2 * (op.n[4] + op.n[5]) + \
U * op.n[0] * op.n[1] + \
V1 * (op.cdagger[0] * op.c[2] + op.cdagger[2] * op.c[0] + \
op.cdagger[1] * op.c[3] + op.cdagger[3] * op.c[1] ) + \
V2 * (op.cdagger[0] * op.c[4] + op.cdagger[4] * op.c[0] + \
op.cdagger[1] * op.c[5] + op.cdagger[5] * op.c[1] )
# ------------------------------------------------------------------
# -- compare
compare_sparse_matrices(H_mat, H_ref)
def test_sparse_matrix_representation():
up, do = 0, 1
fundamental_operators = [c(up, 0), c(do, 0)]
rep = SparseMatrixRepresentation(fundamental_operators)
# -- Test an operator
O_mat = rep.sparse_matrix(c(up, 0))
O_ref = rep.sparse_operators.c_dag[0].getH()
compare_sparse_matrices(O_mat, O_ref)
# -- Test
O_mat = rep.sparse_matrix(c(do, 0))
O_ref = rep.sparse_operators.c_dag[1].getH()
compare_sparse_matrices(O_mat, O_ref)
# -- Test expression
H_expr = c(up, 0) * c(do, 0) * c_dag(up, 0) * c_dag(do, 0)
H_mat = rep.sparse_matrix(H_expr)
c_dag0, c_dag1 = rep.sparse_operators.c_dag
c_0, c_1 = c_dag0.getH(), c_dag1.getH()
H_ref = c_0 * c_1 * c_dag0 * c_dag1
compare_sparse_matrices(H_mat, H_ref)
class TriqsExactDiagonalization(object):
""" Exact diagonalization for Triqs operator expressions. """
# ------------------------------------------------------------------
def __init__(self, H, fundamental_operators, beta):
self.beta = beta
self.rep = SparseMatrixRepresentation(fundamental_operators)
self.ed = SparseExactDiagonalization(self.rep.sparse_matrix(H),
self.rep.blocks, beta)
# ------------------------------------------------------------------
def get_expectation_value(self, op):
return self.ed.get_expectation_value(self.rep.sparse_matrix(op))
# ------------------------------------------------------------------
def get_free_energy(self):
return self.ed.get_free_energy()
def get_partition_function(self):
return self.ed.get_partition_function()
def get_density_matrix(self):
return self.ed.get_density_matrix()
def get_ground_state_energy(self):
return self.ed.get_ground_state_energy()
# ------------------------------------------------------------------
def set_g2_tau(self, g_tau, op1, op2):
assert (type(g_tau.mesh) == MeshImTime)
assert (self.beta == g_tau.mesh.beta)
op1_mat = self.rep.sparse_matrix(op1)
op2_mat = self.rep.sparse_matrix(op2)
tau = np.array([tau.value for tau in g_tau.mesh])
g_tau.data[:, 0, 0] = self.ed.get_tau_greens_function_component(
tau, op1_mat, op2_mat)
#self.set_tail(g_tau, op1_mat, op2_mat)
# ------------------------------------------------------------------
def set_g2_tau_matrix(self, g_tau, op_list):
assert (g_tau.target_shape == tuple([len(op_list)] * 2))
for (i1, o1), (i2, o2) in mpi_op_comb(op_list, repeat=2):
self.set_g2_tau(g_tau[i1, i2], o1, dagger(o2))
g_tau = mpi_all_reduce_g(g_tau)
return g_tau
# ------------------------------------------------------------------
def set_g2_iwn(self, g_iwn, op1, op2):
assert (self.beta == g_iwn.mesh.beta)
op1_mat = self.rep.sparse_matrix(op1)
op2_mat = self.rep.sparse_matrix(op2)
iwn = np.array([iwn.value for iwn in g_iwn.mesh])
g_iwn.data[:, 0, 0] = self.ed.get_frequency_greens_function_component(
iwn, op1_mat, op2_mat, self.xi(g_iwn.mesh))
#self.set_tail(g_iwn, op1_mat, op2_mat)
# ------------------------------------------------------------------
def set_g2_iwn_matrix(self, g_iwn, op_list):
assert (g_iwn.target_shape == tuple([len(op_list)] * 2))
for (i1, o1), (i2, o2) in mpi_op_comb(op_list, repeat=2):
self.set_g2_iwn(g_iwn[i1, i2], o1, dagger(o2))
g_iw = mpi_all_reduce_g(g_iwn)
return g_iwn
# ------------------------------------------------------------------
def set_tail(self, g, op1_mat, op2_mat):
tail = g.tail
raw_tail = self.ed.get_high_frequency_tail_coeff_component(
op1_mat, op2_mat, self.xi(g.mesh), Norder=tail.order_max)
for idx in xrange(tail.order_max):
tail[idx + 1] = raw_tail[idx]
# ------------------------------------------------------------------
def xi(self, mesh):
if mesh.statistic == 'Fermion': return -1.0
elif mesh.statistic == 'Boson': return +1.0
else: raise NotImplementedError
# ------------------------------------------------------------------
def set_g3_tau(self, g3_tau, op1, op2, op3):
ops = [op1, op2, op3]
ops_mat = np.array([self.rep.sparse_matrix(op) for op in ops])
for idxs, taus, perm, perm_sign in SquareTrianglesMesh(g3_tau):
ops_perm_mat = ops_mat[perm + [2]]
taus_perm = np.array(taus).T[perm]
data = self.ed.get_timeordered_two_tau_greens_function(
taus_perm, ops_perm_mat)
for idx, d in zip(idxs, data):
g3_tau[Idxs(idx)] = perm_sign * d
# ------------------------------------------------------------------
def set_g40_tau(self, g40_tau, g_tau):
assert (type(g_tau.mesh) == MeshImTime)
assert (g_tau.target_shape == (1, 1, 1, 1))
for t1, t2, t3 in g40_tau.mesh:
g40_tau[t1, t2, t3] = g_tau(t1 - t2) * g_tau(t3.value) - g_tau(
t1.value) * g_tau(t3 - t2)
# ------------------------------------------------------------------
def set_g40_tau_matrix(self, g40_tau, g_tau):
assert (type(g_tau.mesh) == MeshImTime)
assert (g_tau.target_shape == g40_tau.target_shape[:2])
assert (g_tau.target_shape == g40_tau.target_shape[2:])
for t1, t2, t3 in g40_tau.mesh:
g40_tau[t1, t2, t3] *= 0.
g40_tau[t1, t2, t3] += np.einsum('ba,dc->abcd', g_tau(t1 - t2),
g_tau(t3.value))
g40_tau[t1, t2, t3] -= np.einsum('da,bc->abcd', g_tau(t1.value),
g_tau(t3 - t2))
# ------------------------------------------------------------------
def set_g4_tau(self, g4_tau, op1, op2, op3, op4):
ops = [op1, op2, op3, op4]
ops_mat = np.array([self.rep.sparse_matrix(op) for op in ops])
for idxs, taus, perm, perm_sign in CubeTetrasMesh(g4_tau):
ops_perm_mat = ops_mat[perm + [3]]
taus_perm = np.array(taus).T[perm]
data = self.ed.get_timeordered_three_tau_greens_function(
taus_perm, ops_perm_mat)
for idx, d in zip(idxs, data):
g4_tau[Idxs(idx)] = perm_sign * d
# ------------------------------------------------------------------
def set_g4_tau_matrix(self, g4_tau, op_list):
assert (g4_tau.target_shape == tuple([len(op_list)] * 4))
for (i1, o1), (i2, o2), (i3, o3), (i4, o4) in \
mpi_op_comb(op_list, repeat=4):
self.set_g4_tau(g4_tau[i1, i2, i3, i4], o1, dagger(o2), o3,
dagger(o4))
g4_tau = mpi_all_reduce_g(g4_tau)
return g4_tau
class TriqsExactDiagonalization(object):
""" Exact diagonalization for Triqs operator expressions. """
# ------------------------------------------------------------------
def __init__(self, H, fundamental_operators, beta):
self.beta = beta
self.rep = SparseMatrixRepresentation(fundamental_operators)
self.ed = SparseExactDiagonalization(self.rep.sparse_matrix(H), beta)
# ------------------------------------------------------------------
def get_expectation_value(self, op):
return self.ed.get_expectation_value(self.rep.sparse_matrix(op))
# ------------------------------------------------------------------
def get_free_energy(self):
return self.ed.get_free_energy()
def get_partition_function(self):
return self.ed.get_partition_function()
def get_density_matrix(self):
return self.ed.get_density_matrix()
def get_ground_state_energy(self):
return self.ed.get_ground_state_energy()
# ------------------------------------------------------------------
def set_g2_tau(self, g_tau, op1, op2):
assert (type(g_tau.mesh) == MeshImTime)
assert (self.beta == g_tau.mesh.beta)
assert (g_tau.target_shape == (1, 1))
op1_mat = self.rep.sparse_matrix(op1)
op2_mat = self.rep.sparse_matrix(op2)
tau = np.array([tau for tau in g_tau.mesh])
g_tau.data[:, 0, 0] = \
self.ed.get_tau_greens_function_component(
tau, op1_mat, op2_mat)
self.set_tail(g_tau, op1_mat, op2_mat)
# ------------------------------------------------------------------
def set_g2_iwn(self, g_iwn, op1, op2):
assert (self.beta == g_iwn.mesh.beta)
assert (g_iwn.target_shape == (1, 1))
op1_mat = self.rep.sparse_matrix(op1)
op2_mat = self.rep.sparse_matrix(op2)
iwn = np.array([iwn for iwn in g_iwn.mesh])
g_iwn.data[:, 0, 0] = \
self.ed.get_frequency_greens_function_component(
iwn, op1_mat, op2_mat, self.xi(g_iwn.mesh))
self.set_tail(g_iwn, op1_mat, op2_mat)
# ------------------------------------------------------------------
def set_tail(self, g, op1_mat, op2_mat):
tail = g.tail
raw_tail = self.ed.get_high_frequency_tail_coeff_component(
op1_mat, op2_mat, self.xi(g.mesh), Norder=tail.order_max)
for idx in xrange(tail.order_max):
tail[idx + 1][:] = raw_tail[idx]
# ------------------------------------------------------------------
def xi(self, mesh):
if mesh.statistic == 'Fermion': return -1.0
elif mesh.statistic == 'Boson': return +1.0
else: raise NotImplementedError
# ------------------------------------------------------------------
def set_g3_tau(self, g3_tau, op1, op2, op3):
assert (g3_tau.target_shape == (1, 1, 1, 1))
op1_mat = self.rep.sparse_matrix(op1)
op2_mat = self.rep.sparse_matrix(op2)
op3_mat = self.rep.sparse_matrix(op3)
ops_mat = np.array([op1_mat, op2_mat, op3_mat])
for idxs, taus, perm, perm_sign in SquareTrianglesMesh(g3_tau):
ops_perm_mat = ops_mat[perm + [2]]
taus_perm = np.array(taus).T[perm]
data = self.ed.get_timeordered_two_tau_greens_function(
taus_perm, ops_perm_mat)
for idx, d in zip(idxs, data):
g3_tau[list(idx)][:] = perm_sign * d
# ------------------------------------------------------------------
def set_g40_tau(self, g40_tau, g_tau):
assert (type(g_tau.mesh) == MeshImTime)
#assert( g_tau.target_shape == g40_tau.target_shape )
for (i1, i2, i3), (t1, t2, t3) in enumerate_tau3(g40_tau):
g40_tau[[i1, i2, i3]][:] = \
g_tau(t1-t2)*g_tau(t3) - g_tau(t1)*g_tau(t3-t2)
# ------------------------------------------------------------------
def set_g4_tau(self, g4_tau, op1, op2, op3, op4):
assert (g4_tau.target_shape == (1, 1, 1, 1))
op1_mat = self.rep.sparse_matrix(op1)
op2_mat = self.rep.sparse_matrix(op2)
op3_mat = self.rep.sparse_matrix(op3)
op4_mat = self.rep.sparse_matrix(op4)
ops_mat = np.array([op1_mat, op2_mat, op3_mat, op4_mat])
for idxs, taus, perm, perm_sign in CubeTetrasMesh(g4_tau):
ops_perm_mat = ops_mat[perm + [3]]
taus_perm = np.array(taus).T[perm]
data = self.ed.get_timeordered_three_tau_greens_function(
taus_perm, ops_perm_mat)
for idx, d in zip(idxs, data):
g4_tau[list(idx)][:] = perm_sign * d