def test_cf_G_tau_and_G_iw_nonint(verbose=False):
beta = 3.22
eps = 1.234
niw = 64
ntau = 2 * niw + 1
H = eps * c_dag(0,0) * c(0,0)
fundamental_operators = [c(0,0)]
ed = TriqsExactDiagonalization(H, fundamental_operators, beta)
# ------------------------------------------------------------------
# -- Single-particle Green's functions
G_tau = GfImTime(beta=beta, statistic='Fermion', n_points=ntau, target_shape=(1,1))
G_iw = GfImFreq(beta=beta, statistic='Fermion', n_points=niw, target_shape=(1,1))
G_iw << inverse( iOmega_n - eps )
G_tau << InverseFourier(G_iw)
G_tau_ed = GfImTime(beta=beta, statistic='Fermion', n_points=ntau, target_shape=(1,1))
G_iw_ed = GfImFreq(beta=beta, statistic='Fermion', n_points=niw, target_shape=(1,1))
ed.set_g2_tau(G_tau_ed[0, 0], c(0,0), c_dag(0,0))
ed.set_g2_iwn(G_iw_ed[0, 0], c(0,0), c_dag(0,0))
# ------------------------------------------------------------------
# -- Compare gfs
from pytriqs.utility.comparison_tests import assert_gfs_are_close
assert_gfs_are_close(G_tau, G_tau_ed)
assert_gfs_are_close(G_iw, G_iw_ed)
# ------------------------------------------------------------------
# -- Plotting
if verbose:
from pytriqs.plot.mpl_interface import oplot, plt
subp = [3, 1, 1]
plt.subplot(*subp); subp[-1] += 1
oplot(G_tau.real)
oplot(G_tau_ed.real)
plt.subplot(*subp); subp[-1] += 1
diff = G_tau - G_tau_ed
oplot(diff.real)
oplot(diff.imag)
plt.subplot(*subp); subp[-1] += 1
oplot(G_iw)
oplot(G_iw_ed)
plt.show()
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
# ------------------------------------------------------------------
# -- Single-particle Green's functions
g_tau = GfImTime(name=r'$g$',
beta=beta,
statistic='Fermion',
n_points=50,
indices=[1])
g_iwn = GfImFreq(name='$g$',
beta=beta,
statistic='Fermion',
n_points=10,
indices=[1])
ed.set_g2_tau(g_tau, c(up, 0), c_dag(up, 0))
ed.set_g2_iwn(g_iwn, c(up, 0), c_dag(up, 0))
# ------------------------------------------------------------------
# -- Two particle Green's functions
ntau = 20
imtime = MeshImTime(beta, 'Fermion', ntau)
prodmesh = MeshProduct(imtime, imtime, imtime)
g40_tau = Gf(name='g40_tau', mesh=prodmesh, target_shape=[1, 1, 1, 1])
g4_tau = Gf(name='g4_tau', mesh=prodmesh, target_shape=[1, 1, 1, 1])
ed.set_g40_tau(g40_tau, g_tau)
ed.set_g4_tau(g4_tau, c(up, 0), c_dag(up, 0), c(up, 0), c_dag(up, 0))
beta = 10.0
U = 2.0
mu = 1.0
h = 0.1
#V = 0.5
V = 1.0
epsilon = 2.3
H = U * n('up', 0) * n('do', 0) + \
- mu * (n('up', 0) + n('do', 0)) + \
h * n('up', 0) - h * n('do', 0) + \
epsilon * (n('up', 1) + n('do', 1)) - epsilon * (n('up', 2) + n('do', 2)) + \
V * ( c_dag('up', 0) * c('up', 1) + c_dag('up', 1) * c('up', 0) ) + \
V * ( c_dag('do', 0) * c('do', 1) + c_dag('do', 1) * c('do', 0) ) + \
V * ( c_dag('up', 0) * c('up', 2) + c_dag('up', 2) * c('up', 0) ) + \
V * ( c_dag('do', 0) * c('do', 2) + c_dag('do', 2) * c('do', 0) )
ed = TriqsExactDiagonalization(H, fundamental_operators, beta)
n_tau = 101
G_tau_up = Gf(mesh=MeshImTime(beta, 'Fermion', n_tau), target_shape=[])
G_tau_do = Gf(mesh=MeshImTime(beta, 'Fermion', n_tau), target_shape=[])
ed.set_g2_tau(G_tau_up, c('up', 0), c_dag('up', 0))
ed.set_g2_tau(G_tau_do, c('do', 0), c_dag('do', 0))
with HDFArchive('anderson.pyed.h5', 'w') as Results:
Results['up'] = G_tau_up
Results['dn'] = G_tau_do
c(up,0), c(do,0), c(up,1), c(do,1), c(up,2), c(do,2)]
ed = TriqsExactDiagonalization(H, fundamental_operators, beta)
# ------------------------------------------------------------------
# -- Single-particle Green's functions
g_tau = GfImTime(name=r'$g$', beta=beta,
statistic='Fermion', n_points=50,
target_shape=(1,1))
g_iwn = GfImFreq(name='$g$', beta=beta,
statistic='Fermion', n_points=10,
target_shape=(1,1))
ed.set_g2_tau(g_tau[0,0], c(up,0), c_dag(up,0))
ed.set_g2_iwn(g_iwn[0,0], c(up,0), c_dag(up,0))
# ------------------------------------------------------------------
# -- Two particle Green's functions
ntau = 20
imtime = MeshImTime(beta, 'Fermion', ntau)
prodmesh = MeshProduct(imtime, imtime, imtime)
g40_tau = Gf(name='g40_tau', mesh=prodmesh, target_shape=[1, 1, 1, 1])
g4_tau = Gf(name='g4_tau', mesh=prodmesh, target_shape=[1, 1, 1, 1])
ed.set_g40_tau(g40_tau, g_tau[0,0])
ed.set_g4_tau(g4_tau[0,0,0,0], c(up,0), c_dag(up,0), c(up,0), c_dag(up,0))
def make_calc(U=10):
# ------------------------------------------------------------------
# -- Hubbard atom with two bath sites, Hamiltonian
params = dict(
beta=2.0,
V1=2.0,
V2=5.0,
epsilon1=0.00,
epsilon2=4.00,
mu=2.0,
U=U,
ntau=40,
niw=15,
)
# ------------------------------------------------------------------
class Dummy():
def __init__(self):
pass
d = Dummy() # storage space
d.params = params
print '--> Solving SIAM with parameters'
for key, value in params.items():
print '%10s = %-10s' % (key, str(value))
globals()[key] = value # populate global namespace
# ------------------------------------------------------------------
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)
d.H = -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) )
# ------------------------------------------------------------------
# -- Exact diagonalization
fundamental_operators = [
c(up, 0), c(do, 0),
c(up, 1), c(do, 1),
c(up, 2), c(do, 2)
]
ed = TriqsExactDiagonalization(d.H, fundamental_operators, beta)
# ------------------------------------------------------------------
# -- Single-particle Green's functions
Gopt = dict(beta=beta, statistic='Fermion', indices=[1])
d.G_tau = GfImTime(name=r'$G(\tau)$', n_points=ntau, **Gopt)
d.G_iw = GfImFreq(name='$G(i\omega_n)$', n_points=niw, **Gopt)
ed.set_g2_tau(d.G_tau, c(up, 0), c_dag(up, 0))
ed.set_g2_iwn(d.G_iw, c(up, 0), c_dag(up, 0))
# chi2pp = + < c^+_u(\tau^+) c_u(0^+) c^+_d(\tau) c_d(0) >
# = - < c^+_u(\tau^+) c^+_d(\tau) c_u(0^+) c_d(0) >
chi2opt = dict(beta=beta, statistic='Fermion', indices=[1], n_points=ntau)
d.chi2pp_tau = GfImTime(name=r'$\chi^{(2)}_{PP}(\tau)$', **chi2opt)
ed.set_g2_tau(d.chi2pp_tau,
c_dag(up, 0) * c_dag(do, 0),
c(up, 0) * c(do, 0))
d.chi2pp_tau *= -1.0 * -1.0 # commutation sign and gf sign
d.chi2pp_iw = g_iw_from_tau(d.chi2pp_tau, niw)
# chi2ph = < c^+_u(\tau^+) c_u(\tau) c^+_d(0^+) c_d(0) >
d.chi2ph_tau = GfImTime(name=r'$\chi^{(2)}_{PH}(\tau)$', **chi2opt)
#d.chi2ph_tau = Gf(name=r'$\chi^{(2)}_{PH}(\tau)$', **chi2opt)
ed.set_g2_tau(d.chi2ph_tau,
c_dag(up, 0) * c(up, 0),
c_dag(do, 0) * c(do, 0))
d.chi2ph_tau *= -1.0 # gf sign
d.chi2ph_iw = g_iw_from_tau(d.chi2ph_tau, niw)
# ------------------------------------------------------------------
# -- Two particle Green's functions
imtime = MeshImTime(beta, 'Fermion', ntau)
prodmesh = MeshProduct(imtime, imtime, imtime)
G2opt = dict(mesh=prodmesh, target_shape=[1, 1, 1, 1])
d.G02_tau = Gf(name='$G^{(2)}_0(\tau_1, \tau_2, \tau_3)$', **G2opt)
ed.set_g40_tau(d.G02_tau, d.G_tau)
d.G02_iw = chi4_iw_from_tau(d.G02_tau, niw)
d.G2_tau = Gf(name='$G^{(2)}(\tau_1, \tau_2, \tau_3)$', **G2opt)
ed.set_g4_tau(d.G2_tau, c_dag(up, 0), c(up, 0), c_dag(do, 0), c(do, 0))
#ed.set_g4_tau(d.G2_tau, c(up,0), c_dag(up,0), c(do,0), c_dag(do,0)) # <cc^+cc^+>
d.G2_iw = chi4_iw_from_tau(d.G2_tau, niw)
# -- trying to fix the bug in the fft for w2
d.G02_iw.data[:] = d.G02_iw.data[:, ::-1, ...].conj()
d.G2_iw.data[:] = d.G2_iw.data[:, ::-1, ...].conj()
# ------------------------------------------------------------------
# -- 3/2-particle Green's functions (equal times)
prodmesh = MeshProduct(imtime, imtime)
chi3opt = dict(mesh=prodmesh, target_shape=[1, 1, 1, 1])
# chi3pp = <c^+_u(\tau) c_u(0^+) c^+_d(\tau') c_d(0) >
# = - <c^+_u(\tau) c^+_d(\tau') c_u(0^+) c_d(0) >
d.chi3pp_tau = Gf(name='$\Chi^{(3)}_{PP}(\tau_1, \tau_2, \tau_3)$',
**chi3opt)
ed.set_g3_tau(d.chi3pp_tau, c_dag(up, 0), c_dag(do, 0),
c(up, 0) * c(do, 0))
d.chi3pp_tau *= -1.0 # from commutation
d.chi3pp_iw = chi3_iw_from_tau(d.chi3pp_tau, niw)
# chi3ph = <c^+_u(\tau) c_u(\tau') c^+_d(0^+) c_d(0) >
d.chi3ph_tau = Gf(name='$\Chi^{(3)}_{PH}(\tau_1, \tau_2, \tau_3)$',
**chi3opt)
ed.set_g3_tau(d.chi3ph_tau, c_dag(up, 0), c(up, 0),
c_dag(do, 0) * c(do, 0))
d.chi3ph_iw = chi3_iw_from_tau(d.chi3ph_tau, niw)
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_ed.h5'
with HDFArchive(filename, 'w') as res:
for key, value in d.__dict__.items():
res[key] = value
def test_two_particle_greens_function():
# ------------------------------------------------------------------
# -- 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 = 0.0
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 = -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))
# ------------------------------------------------------------------
# -- Exact diagonalization
fundamental_operators = [
c(up, 0), c(do, 0),
c(up, 1), c(do, 1),
c(up, 2), c(do, 2)
]
ed = TriqsExactDiagonalization(H, fundamental_operators, beta)
# ------------------------------------------------------------------
# -- single particle Green's functions
g_tau = GfImTime(name=r'$g$',
beta=beta,
statistic='Fermion',
n_points=100,
target_shape=(1, 1))
ed.set_g2_tau(g_tau[0, 0], c(up, 0), c_dag(up, 0))
# ------------------------------------------------------------------
# -- Two particle Green's functions
ntau = 10
imtime = MeshImTime(beta, 'Fermion', ntau)
prodmesh = MeshProduct(imtime, imtime, imtime)
g40_tau = Gf(name='g40_tau', mesh=prodmesh, target_shape=(1, 1, 1, 1))
g4_tau = Gf(name='g4_tau', mesh=prodmesh, target_shape=(1, 1, 1, 1))
ed.set_g40_tau_matrix(g40_tau, g_tau)
ed.set_g4_tau(g4_tau[0, 0, 0, 0], c(up, 0), c_dag(up, 0), c(up, 0),
c_dag(up, 0))
# ------------------------------------------------------------------
# -- compare
zero_outer_planes_and_equal_times(g4_tau)
zero_outer_planes_and_equal_times(g40_tau)
np.testing.assert_array_almost_equal(g4_tau.data, g40_tau.data)
fundamental_operators = [
c(up, 0), c(do, 0),
c(up, 1), c(do, 1),
c(up, 2), c(do, 2)
]
ed = TriqsExactDiagonalization(H, fundamental_operators, beta)
# ------------------------------------------------------------------
# -- Single-particle Green's functions
g_tau = GfImTime(name=r'$g$',
beta=beta,
statistic='Fermion',
n_points=500,
indices=['A', 'B'])
for (i1, s1), (i2, s2) in itertools.product([('A', up), ('B', do)],
repeat=2):
print i1, s1, i2, s2
ed.set_g2_tau(g_tau[i1, i2], c(s1, 0), c_dag(s2, 0))
# ------------------------------------------------------------------
# -- Store to hdf5
with HDFArchive('data_ed.h5', 'w') as res:
res['tot'] = g_tau
# ----------------------------------------------------------------------
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
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
# ------------------------------------------------------------------
# -- Store to hdf5
if mpi.is_master_node():
with HDFArchive('data_pyed.h5', 'w') as res:
res['p'] = p
T_imp = block_diag(T_imp, T_imp)
T_bath = block_diag(T_bath, T_bath)
print 'V =\n', V
print 'T_imp =\n', T_imp
print 'T_bath =\n', T_bath
T = np.block([[T_imp, V], [V.T, T_bath]])
print 'T =\n', T
H_int = h_int_kanamori(spin_names, imp_idxs,
np.array([[0, U - 3 * J], [U - 3 * J, 0]]),
np.array([[U, U - 2 * J], [U - 2 * J, U]]), J, True)
H = H_int + get_quadratic_operator(T, fop)
ed = TriqsExactDiagonalization(H, fop, beta)
n_tau = 101
G_tau_up = Gf(mesh=MeshImTime(beta, 'Fermion', n_tau), target_shape=[2, 2])
G_tau_do = Gf(mesh=MeshImTime(beta, 'Fermion', n_tau), target_shape=[2, 2])
for i1, i2 in itertools.product(range(norb), repeat=2):
ed.set_g2_tau(G_tau_up[i1, i2], c('up', i1), c_dag('up', i2))
ed.set_g2_tau(G_tau_do[i1, i2], c('do', i1), c_dag('do', i2))
with HDFArchive('kanamori_offdiag.pyed.h5', 'w') as Results:
Results['up'] = G_tau_up
Results['dn'] = G_tau_do