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)
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)