def make_calc(beta=2.0, h_field=0.0):
# ------------------------------------------------------------------
# -- Hubbard atom with two bath sites, Hamiltonian
p = ParameterCollection(
beta = beta,
h_field = h_field,
U = 5.0,
ntau = 40,
niw = 15,
)
p.mu = 0.5*p.U
# ------------------------------------------------------------------
print '--> Solving SIAM with parameters'
print p
# ------------------------------------------------------------------
up, do = 'up', 'dn'
docc = c_dag(up,0) * c(up,0) * c_dag(do,0) * c(do,0)
mA = 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)
p.H = -p.mu * nA + p.U * docc + p.h_field * mA
# ------------------------------------------------------------------
fundamental_operators = [c(up,0), c(do,0)]
ed = TriqsExactDiagonalization(p.H, fundamental_operators, p.beta)
g_tau = GfImTime(beta=beta, statistic='Fermion', n_points=40, indices=[0])
g_iw = GfImFreq(beta=beta, statistic='Fermion', n_points=10, indices=[0])
p.G_tau = BlockGf(name_list=[up,do], block_list=[g_tau]*2, make_copies=True)
p.G_iw = BlockGf(name_list=[up,do], block_list=[g_iw]*2, make_copies=True)
ed.set_g2_tau(p.G_tau[up], c(up,0), c_dag(up,0))
ed.set_g2_tau(p.G_tau[do], c(do,0), c_dag(do,0))
ed.set_g2_iwn(p.G_iw[up], c(up,0), c_dag(up,0))
ed.set_g2_iwn(p.G_iw[do], c(do,0), c_dag(do,0))
p.magnetization = ed.get_expectation_value(0.5 * mA)
p.magnetization2 = ed.get_expectation_value(0.25 * mA * mA)
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_pyed_h_field_%4.4f.h5' % h_field
with HDFArchive(filename,'w') as res:
res['p'] = p
O1 = dagger(o1) * o2
O1 = O1 + dagger(O1)
ed_p = TriqsExactDiagonalization(m.H + F * O1, m.op_full, m.beta)
ed_m = TriqsExactDiagonalization(m.H - F * O1, m.op_full, m.beta)
p.g_tau_field[(i1, i2)] = g_tau.copy()
ed_p.set_g2_tau_matrix(p.g_tau_field[(i1, i2)], m.op_imp)
for i3, i4 in itertools.product(range(4), repeat=2):
o3, o4 = m.op_imp[i3], m.op_imp[i4]
O2 = dagger(o3) * o4
O2_vec = np.zeros(2, dtype=np.complex)
O2_vec[0] = ed_m.get_expectation_value(O2)
O2_vec[1] = ed_p.get_expectation_value(O2)
p.chi_field[i1, i2, i3, i4] = -(O2_vec[1] - O2_vec[0])/(2*F)
p.chi_field[i2, i1, i3, i4] = p.chi_field[i1, i2, i3, i4]
chi_tau = p.chi[i1, i2, i3, i4] + p.chi[i2, i1, i3, i4]
chi_field = p.chi_field[i1, i2, i3, i4]
np.testing.assert_almost_equal(chi_tau, chi_field, decimal=3)
if(np.abs(chi_tau.real) > 1e-6):
print i1, i2, i3, i4
print 'chi_tau = %+2.6f' % chi_tau.real
print 'chi_field = %+2.6f' % chi_field.real
print 'diff = %+2.6E' % (chi_field.real - chi_tau.real)
def make_calc(beta=2.0, h_field=0.0):
# ------------------------------------------------------------------
# -- Hubbard atom with two bath sites, Hamiltonian
p = ParameterCollection(
beta=beta,
V1=2.0,
V2=5.0,
epsilon1=0.10,
epsilon2=3.00,
h_field=h_field,
mu=0.0,
U=5.0,
ntau=800,
niw=15,
)
# ------------------------------------------------------------------
print '--> Solving SIAM with parameters'
print p
# ------------------------------------------------------------------
up, do = 'up', 'dn'
docc = c_dag(up, 0) * c(up, 0) * c_dag(do, 0) * c(do, 0)
mA = 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)
p.H = -p.mu * nA + p.U * docc + p.h_field * mA + \
p.epsilon1 * nB + p.epsilon2 * nC + \
p.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) ) + \
p.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)
]
ed = TriqsExactDiagonalization(p.H, fundamental_operators, p.beta)
g_tau = GfImTime(beta=beta, statistic='Fermion', n_points=400, indices=[0])
g_iw = GfImFreq(beta=beta, statistic='Fermion', n_points=10, indices=[0])
p.G_tau = BlockGf(name_list=[up, do],
block_list=[g_tau] * 2,
make_copies=True)
p.G_iw = BlockGf(name_list=[up, do],
block_list=[g_iw] * 2,
make_copies=True)
ed.set_g2_tau(p.G_tau[up][0, 0], c(up, 0), c_dag(up, 0))
ed.set_g2_tau(p.G_tau[do][0, 0], c(do, 0), c_dag(do, 0))
ed.set_g2_iwn(p.G_iw[up][0, 0], c(up, 0), c_dag(up, 0))
ed.set_g2_iwn(p.G_iw[do][0, 0], c(do, 0), c_dag(do, 0))
p.magnetization = ed.get_expectation_value(0.5 * mA)
p.O_tau = Gf(mesh=MeshImTime(beta, 'Fermion', 400), target_shape=[])
ed.set_g2_tau(p.O_tau, n(up, 0), n(do, 0))
p.O_tau.data[:] *= -1.
p.exp_val = ed.get_expectation_value(n(up, 0) * n(do, 0))
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_pyed_h_field_%4.4f.h5' % h_field
with HDFArchive(filename, 'w') as res:
res['p'] = p
target_shape=(4, 4, 4, 4))
p.chi = np.zeros_like(p.chi_static)
tau = np.array([float(tau) for tau in p.chi_tau.mesh])
for i1, i2, i3, i4, in itertools.product(range(4), repeat=4):
print i1, i2, i3, i4
o1, o2, o3, o4 = m.op_imp[i1], m.op_imp[i2], m.op_imp[i3], m.op_imp[i4]
O1 = dagger(o1) * o2
O2 = dagger(o3) * o4
p.O1_exp[i1, i2] = ed.get_expectation_value(O1)
p.O2_exp[i3, i4] = ed.get_expectation_value(O2)
p.chi_dissconn[i1, i2, i3, i4] = p.O1_exp[i1, i2] * p.O2_exp[i3, i4]
p.chi_static[i1, i2, i3, i4] = ed.get_expectation_value(O1 * O2)
ed.set_g2_tau(p.chi_tau[i1, i2, i3, i4], O1, O2)
chi_tau = p.chi_tau[i1, i2, i3, i4]
chi_tau *= -1. # cancel gf -1 prefactor
chi_dissconn = p.chi_dissconn[i1, i2, i3, i4]
chi_tau.data[:] -= chi_dissconn
p.chi[i1, i2, i3, i4] = np.trapz(chi_tau.data, x=tau) / m.beta