def get_tb_model(t, U, n, m, mu=0., vanilla_tb=False):
h_loc = -U * m * np.diag([+1., -1.]) + (0.5 * U * n - mu) * np.eye(2)
T = -t * np.eye(2)
if vanilla_tb:
from pytriqs.lattice.tight_binding import TBLattice
else:
from triqs_tprf.tight_binding import TBLattice
t_r = TBLattice(
units=[(1, 0, 0)],
hopping={
# nearest neighbour hopping -t
(
0, ): h_loc,
(+1, ): T,
(-1, ): T,
},
orbital_positions=[(0, 0, 0)] * 2,
orbital_names=['up', 'do'],
)
return t_r
S = Solver(beta=beta, gf_struct=[('up', [0]), ('down', [0])])
h_int = U * n('up', 0) * n('down', 0) #local interating hamiltonian
hop = {
(1, 0): [[t]],
(-1, 0): [[t]],
(0, 1): [[t]],
(0, -1): [[t]],
(1, 1): [[tp]],
(-1, -1): [[tp]],
(1, -1): [[tp]],
(-1, 1): [[tp]]
}
L = TBLattice(units=[(1, 0, 0), (0, 1, 0)],
hopping=hop,
orbital_names=range(1),
orbital_positions=[(0., 0., 0.)] * 1)
SL = TBSuperLattice(tb_lattice=L, super_lattice_units=[(1, 1, 0), (1, -1, 0)])
SK = SumkDiscreteFromLattice(lattice=SL, n_points=nk)
mesh = S.G_iw.mesh
Gloc = BlockGf(name_block_generator=[
(s, GfImFreq(indices=SK.GFBlocIndices, mesh=mesh)) for s in ['up', 'down']
],
make_copies=False)
Sigma_lat = Gloc.copy()
#function to extract density for a given mu, to be used by dichotomy function to determine mu
def Dens(mu):
dens = SK(mu=mu, Sigma=Sigma_lat).total_density()
t = -1.00 # First neighbour Hopping
tp = 0.0 * t # Second neighbour Hopping
hop = {
(1, 0): [
[t]
], # Hopping[ Displacement on the lattice] = [[t11, t12, t13....], [t21, t22, t23....], ..., [...., tnn]]
(-1, 0): [[t]], # where n=Number_Orbitals
(0, 1): [[t]],
(0, -1): [[t]],
(1, 1): [[tp]],
(-1, -1): [[tp]],
(1, -1): [[tp]],
(-1, 1): [[tp]]
}
L = TBLattice(units=[(1, 0, 0), (0, 1, 0)], hopping=hop)
SL = TBSuperLattice(tb_lattice=L, super_lattice_units=[(2, 0), (0, 2)])
# SumK function that will perform the sum over the BZ
SK = SumkDiscreteFromLattice(lattice=SL, n_points=8, method="Riemann")
# Defines G and Sigma with a block structure compatible with the SumK function
G = BlockGf(name_block_generator=[(s,
GfImFreq(indices=SK.GFBlocIndices,
mesh=S.G.mesh))
for s in ['up', 'down']],
make_copies=False)
Sigma = G.copy()
# Init Sigma
for n, B in S.Sigma: