#DMFT calculation for a hubbard model on a 2D square lattice

#creates a supercell and allows for anti-ferromagnetism

#uses Triqs version 2.2

from pytriqs.sumk import *

from pytriqs.gf import *

from pytriqs.lattice.tight_binding import TBLattice

from pytriqs.lattice.super_lattice import TBSuperLattice

import pytriqs.utility.mpi as mpi

from pytriqs.utility.dichotomy import dichotomy

from triqs_cthyb import *

from pytriqs.archive import HDFArchive

from pytriqs.operators import *

beta = 40.

t = -1. #nearest neighbor hopping

tp = 0. #next nearest neighbor hopping

U = 3 # hubbard U parameter

nloops = 15 # number of DMFT loops

nk = 30 # number of k points in each dimension

density_required = 1. # target density for setting the chemical potential

outfile = 'U%.1f_afm'%U

p = {}

# solver

p["random_seed"] = 123 * mpi.rank + 567

p["length_cycle"] = 200

p["n_warmup_cycles"] = int(5e4)

p["n_cycles"] = int(1e7/mpi.size)

# tail fit

p["perform_tail_fit"] = True

p["fit_max_moment"] = 4

p["fit_min_w"] = 5

p["fit_max_w"] = 15

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]],

(-1,1) : [[ 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):

return dens.real

#check if there are previous runs in the outfile and if so restart from there

previous_runs = 0

previous_present = False

mu = 0.

if mpi.is_master_node():

ar = HDFArchive(outfile+'.h5','a')

if 'iterations' in ar:

previous_present = True

previous_runs = ar['iterations']

S.Sigma_iw = ar['Sigma_iw']

mu = ar['mu-%d'%previous_runs]

del ar

previous_runs = mpi.bcast(previous_runs)

previous_present = mpi.bcast(previous_present)

S.Sigma_iw = mpi.bcast(S.Sigma_iw)

mu = mpi.bcast(mu)

for iteration_number in range(1,nloops+1):

it = iteration_number + previous_runs

if mpi.is_master_node():

print('-----------------------------------------------')

print("Iteration = %s"%it)

print('-----------------------------------------------')

if it > 1:

#set the lattice self energy from the impurity self energy

Sigma_lat['up'].data[:,0,0] = S.Sigma_iw['up'].data[:,0,0]

Sigma_lat['down'].data[:,0,0] = S.Sigma_iw['down'].data[:,0,0]

#switch the up and down self energy for the second site

Sigma_lat['up'].data[:,1,1] = S.Sigma_iw['down'].data[:,0,0]

Sigma_lat['down'].data[:,1,1] = S.Sigma_iw['up'].data[:,0,0]

mu, density = dichotomy(Dens, mu, density_required, 1e-4, .5, max_loops = 100, x_name="chemical potential", y_name="density", verbosity=3)

Gloc << SK(mu = mu, Sigma = Sigma_lat)

Gloc1 = S.G_iw.copy() #Gloc for one of the sites

Gloc1['up'].data[:,0,0] = Gloc['up'].data[:,0,0]

Gloc1['down'].data[:,0,0] = Gloc['down'].data[:,0,0]

nlat = Gloc1.total_density().real # lattice density

# set starting guess for Sigma = U/2 at first iteration

if it == 1:

S.Sigma_iw << .5*U

S.G0_iw << inverse(S.Sigma_iw + inverse(Gloc1))

S.solve(h_int=h_int, **p)

#force self energy obtained from solver to be hermitian

for name, s_iw in S.Sigma_iw:

S.Sigma_iw[name] = make_hermitian(s_iw)

nimp = S.G_iw.total_density().real #impurity density

if mpi.is_master_node():

ar = HDFArchive(outfile+'.h5','a')

ar['iterations'] = it

ar['G_0'] = S.G0_iw

ar['G_tau'] = S.G_tau

ar['G_iw'] = S.G_iw

ar['Sigma_iw'] = S.Sigma_iw

ar['Sigma_-%s'%it] = S.Sigma_iw

ar['nimp-%s'%it] = nimp

ar['nlat-%s'%it] = nlat

ar['mu-%s'%it] = mu

del ar