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
def test_sumk_discrete(self):
tbl_w90 = TB_from_wannier90(seed='wannier_TB_test',
path='./',
extend_to_spin=False)
SK = SumkDiscreteFromLattice(lattice=tbl_w90, n_points=10)
Sigma_proto = GfImFreq(
mesh=MeshImFreq(beta=40, S='Fermion', n_max=1025),
target_shape=[tbl_w90.n_orbitals, tbl_w90.n_orbitals])
Sigma_iw = BlockGf(name_list=['up', 'down'],
block_list=[Sigma_proto, Sigma_proto],
make_copies=True)
# Sumk only accepts Sigma of MeshImFreq
Gloc = SK(Sigma=Sigma_iw, mu=12.3461)
# check if density is close to 1, not to strict since nkpts is relatively small
assert abs(Gloc.total_density().real - 1.0) < 1e-2
# -- 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=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])
from triqs.gf import GfImFreq, SemiCircular g = GfImFreq(indices=['eg1', 'eg2'], beta=50, n_points=1000, name="egBlock") g['eg1', 'eg1'] = SemiCircular(half_bandwidth=1) g['eg2', 'eg2'] = SemiCircular(half_bandwidth=2) from triqs.plot.mpl_interface import oplot, plt oplot(g, '-o', x_window=(0, 10)) plt.ylim(-2, 1)
# Import the Green's functions
from triqs.gf import GfImFreq, iOmega_n, inverse
# Create the Matsubara-frequency Green's function and initialize it
g = GfImFreq(indices=[1], beta=50, n_points=1000, name="$G_\mathrm{imp}$")
g << inverse(iOmega_n + 0.5)
from triqs.plot.mpl_interface import oplot
oplot(g, '-o', x_window=(0, 10))
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You may obtain a copy of the License at
# https:#www.gnu.org/licenses/gpl-3.0.txt
#
# Authors: Olivier Parcollet, Nils Wentzell
# Import the Green's functions
from triqs.gf import GfImFreq, iOmega_n, inverse
# Create the Matsubara-frequency Green's function and initialize it
g = GfImFreq(indices=[1], beta=50, n_points=1000, name="imp")
g << inverse(iOmega_n + 0.5)
import triqs.utility.mpi as mpi
mpi.bcast(g)
#Block
from triqs.gf import *
g1 = GfImFreq(indices=['eg1', 'eg2'], beta=50, n_points=1000, name="egBlock")
g2 = GfImFreq(indices=['t2g1', 't2g2', 't2g3'],
beta=50,
n_points=1000,
name="t2gBlock")
G = BlockGf(name_list=('eg', 't2g'), block_list=(g1, g2), make_copies=False)
from triqs.plot.mpl_interface import oplot
from triqs.gf import GfImFreq, Omega, inverse
g = GfImFreq(indices=[0], beta=300, n_points=1000, name="g")
g << inverse(Omega + 0.5)
# the data we want to fit...
# The green function for omega \in [0,0.2]
X, Y = g.x_data_view(x_window=(0, 0.2), flatten_y=True)
from triqs.fit import Fit, linear, quadratic
fitl = Fit(X, Y.imag, linear)
fitq = Fit(X, Y.imag, quadratic)
oplot(g, '-o', x_window=(0, 5))
oplot(fitl, '-x', x_window=(0, 0.5))
oplot(fitq, '-x', x_window=(0, 1))
# a bit more complex, we want to fit with a one fermion level ....
# Cf the definition of linear and quadratic in the lib
one_fermion_level = lambda X, a, b: 1 / (a * X * 1j + b
), r"${1}/(%f x + %f)$", (1, 1)
fit1 = Fit(X, Y, one_fermion_level)
oplot(fit1, '-x', x_window=(0, 3))
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 << Fourier(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 triqs.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 triqs.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()