from pytriqs.utility.comparison_tests import *
# for the imaginary GFs
beta = 40
n_tau = 5001
H = np.array([[0, 0.1j], [-0.1j, 0]])
# construct the atomic GF by hand:
# G_tau = inverse_fourier( (iOmega - H)^(-1) )
G_iw = GfImFreq(beta=beta, indices=[0, 1])
G_iw << iOmega_n - H
G_iw.invert()
G_tau = GfImTime(beta=beta, indices=[0, 1], n_points=n_tau)
G_tau.set_from_inverse_fourier(G_iw)
# construct the Hamiltonian as operator
H_op = Operator()
for i in range(H.shape[0]):
for j in range(H.shape[1]):
H_op += H[i, j] * c_dag('ud', i) * c('ud', j)
# initialize the atomic diagonalization
AD = AtomDiag(H_op, [('ud', 0), ('ud', 1)])
# atomic G(tau) from solver
G_at = atomic_gf(AD, beta, {'ud': [0, 1]}, n_tau)
assert_gfs_are_close(G_at['ud'], G_tau)
[ 0.0-0.1j ,-0.2+0.j , 0.1+0.j , 0.5+0.j ],
[ 0.5+0.j , 0.1+0.j , 0.0+0.j , 0.0+0.j ],
[ 0.1+0.j , 0.5+0.j , 0.0+0.j , 0.0+0.j ]]
H_matrix = np.array(H_matrix)
# fops for the AtomDiag solver
fops = []
for i in range(H_matrix.shape[0]):
fops.append(('ud',i))
H = Operator()
for i in range(H_matrix.shape[0]):
for j in range(H_matrix.shape[1]):
H += H_matrix[i,j] * c_dag('ud',i)*c('ud',j)
# interaction term between the 1st and 2nd orbital
H+=3*n('ud',0)*n('ud',1)
S = AtomDiag(H,fops)
G_tau = atomic_gf(S,beta=10,indices_list={'ud':range(4)},n_tau=41)
with HDFArchive('atomdiag_ed.out.h5','w') as ar:
ar['G_tau']=G_tau
from pytriqs.utility.h5diff import h5diff
# the reference solution was checked against an external ED result
h5diff('atomdiag_ed.ref.h5','atomdiag_ed.out.h5')
# the single-particle Hamiltonian of the problem
H_matrix = [[-0.2 + 0.j, 0.0 + 0.1j, 0.5 + 0.j, 0.1 + 0.j],
[0.0 - 0.1j, -0.2 + 0.j, 0.1 + 0.j, 0.5 + 0.j],
[0.5 + 0.j, 0.1 + 0.j, 0.0 + 0.j, 0.0 + 0.j],
[0.1 + 0.j, 0.5 + 0.j, 0.0 + 0.j, 0.0 + 0.j]]
H_matrix = np.array(H_matrix)
# fops for the AtomDiag solver
fops = []
for i in range(H_matrix.shape[0]):
fops.append(('ud', i))
H = Operator()
for i in range(H_matrix.shape[0]):
for j in range(H_matrix.shape[1]):
H += H_matrix[i, j] * c_dag('ud', i) * c('ud', j)
# interaction term between the 1st and 2nd orbital
H += 3 * n('ud', 0) * n('ud', 1)
S = AtomDiag(H, fops)
G_tau = atomic_gf(S, beta=10, indices_list={'ud': range(4)}, n_tau=41)
with HDFArchive('atomdiag_ed.out.h5', 'w') as ar:
ar['G_tau'] = G_tau
from pytriqs.utility.h5diff import h5diff
# the reference solution was checked against an external ED result
h5diff('atomdiag_ed.ref.h5', 'atomdiag_ed.out.h5')
# for the imaginary GFs
beta = 40
n_tau = 5001
H = np.array([[0,0.1j],[-0.1j,0]])
# construct the atomic GF by hand:
# G_tau = inverse_fourier( (iOmega - H)^(-1) )
G_iw = GfImFreq(beta=beta,indices=[0,1])
G_iw << iOmega_n - H
G_iw.invert()
G_tau = GfImTime(beta=beta,indices=[0,1],n_points=n_tau)
G_tau.set_from_inverse_fourier(G_iw)
# construct the Hamiltonian as operator
H_op = Operator()
for i in range(H.shape[0]):
for j in range(H.shape[1]):
H_op += H[i,j] * c_dag('ud',i)*c('ud',j)
# initialize the atomic diagonalization
AD = AtomDiag(H_op,[('ud',0),('ud',1)])
# atomic G(tau) from solver
G_at = atomic_gf(AD,beta,{'ud':[0,1]},n_tau)
assert_gfs_are_close(G_at['ud'],G_tau)