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hubbard_square_2x2_cdmft_nambu.py
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from pytriqs.gf import *
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 *
import numpy as np
from pytriqs.lattice.tight_binding import TBLattice
from pytriqs.lattice.super_lattice import TBSuperLattice
#script to do 2x2 real space cluster DMFT calculations in the Nambu basis to probe for Superconductivity.
#Force the Self energy to obey D_4 symmetry and the anomalous part to obey dx^2-y^2 symmetry
beta = 5 #inverse temperature
U = 5.6 #Hubbard U parameter
t = -1 #nearest neighbor hopping
tp = 0 #next nearest neighbor hopping
n0 = 1 #density required per site
nk1 = 100 #number of k points in each direction
nloops = 20 #number of DMFT loops
prec_mu = 1e-5 #precision in density required when calculating mu
Delta = 0.01 #inital value of anomalous self energy
outfile = 'beta_%.1f_U%.1f'%(beta, U)
p = {}
# solver
p["random_seed"] = 123 * mpi.rank + 567
p["length_cycle"] = int(2*beta)
p["n_warmup_cycles"] = int(5e4)
p["n_cycles"] = int(2e8/mpi.size)
p["move_double"]= True
p["perform_tail_fit"] = True
p["fit_max_moment"] = 4
p["fit_min_w"] = 5
p["fit_max_w"] = 15
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 = [ (2,0), (0,2)])
mx = 1 #max hopping distance in x direction
my = 1 #max hopping distance in y direction
nx = 2*mx+1
ny = 2*my+1
nk = nk1**2
k1 = [float(i)/nk1 for i in range(nk1)]
kpoints = []
for kx in k1:
for ky in k1:
kpoints.append([kx,ky])
kpoints = np.asarray(kpoints)
Hrij = np.zeros((nx,ny,4,4), dtype = np.complex_)
for r in SL.hopping_dict():
rxind = r[0] + mx
ryind = r[1] + my
Hrij[rxind,ryind] = SL.hopping_dict()[r]
Hk_nambu = np.zeros((nk, 8, 8), dtype = np.complex_)
ikarray = np.array(range(nk))
for ik in (ikarray):
k = kpoints[ik]
Hexp = np.empty_like(Hrij,dtype = np.complex_)
for xi in range(nx):
for yi in range(ny):
r = np.array([xi-mx, yi-my])
eikr = np.exp(-1j*2*np.pi*k.dot(r))
Hexp[xi, yi, :, :] = eikr
Hkrij = Hrij * Hexp
Hk = np.sum(Hkrij, axis = (0,1))
Hk_nambu[ik, :4, :4] = Hk
Hk_nambu[ik, 4:, 4:] = -Hk.T
gloc = GfImFreq(beta = beta, indices=range(8))
Gloc = BlockGf(name_list=['nambu'], block_list=[gloc])
Sigma_orig = Gloc.copy() #self energy in the original site basis
S = Solver(beta = beta, gf_struct = [('s+', [0]), ('s-', [0]), ('d+', [0]), ('d-', [0]), ('px', [0,1]), ('py', [0,1])])
#check for previous iterations and if so restart from last iteration
if mpi.is_master_node():
ar = HDFArchive(outfile+'.h5', 'a')
if 'iterations' in ar:
previous_runs = ar['iterations']
Sigma_orig = ar['Sigma_orig']
mu = ar['mu-%d'%previous_runs]
del ar
else:
mu = 0.
previous_runs = 0
else:
mu = None
previous_runs = None
previous_runs = mpi.bcast(previous_runs)
Sigma_orig = mpi.bcast(Sigma_orig)
mu = mpi.bcast(mu)
a = 0.5
#matrix to change to the (s,d,px,py) basis
Q = np.array([[a, a, a, a, 0, 0, 0, 0],
[0, 0, 0, 0, a, a, a, a],
[a,-a,-a, a, 0, 0, 0, 0],
[0, 0, 0, 0, a,-a,-a, a],
[a,-a, a,-a, 0, 0, 0, 0],
[0, 0, 0, 0, a,-a, a,-a],
[a, a,-a,-a, 0, 0, 0, 0],
[0, 0, 0, 0, a, a,-a,-a]]).T
cs = [c('s+',0), c('s-',0), c('d+',0), c('d-',0), c('px',0), c('px',1), c('py',0), c('py',1)]
cds = [c_dag('s+',0), c_dag('s-',0), c_dag('d+',0), c_dag('d-',0), c_dag('px',0), c_dag('px',1), c_dag('py',0), c_dag('py',1)]
#hamiltonian written in terms of Nambu operators in the (s,d,px,py) basis
h_int = 0
for i in range(4):
for j in range(8):
for k in range(8):
coeff = U*Q[i,j]*Q[i,k]
if abs(coeff) > 1e-8:
h_int += coeff*cds[j]*cs[k]
for l in range(8):
for m in range(8):
coeff = -U*Q[i,j]*Q[i,k]*Q[i+4,l]*Q[i+4,m]
if abs(coeff) > 1e-8:
h_int += coeff*cds[j]*cs[k]*cds[l]*cs[m]
for iteration_number in range(1,nloops+1):
it = iteration_number + previous_runs
if mpi.is_master_node():
print '-----------------------------------------------'
print "Iteration = ", it
print '-----------------------------------------------'
if it == 1:
Sigma_orig['nambu'][0,5] << Delta
Sigma_orig['nambu'][0,6] << -Delta
Sigma_orig['nambu'][1,4] << Delta
Sigma_orig['nambu'][1,7] << -Delta
Sigma_orig['nambu'][2,4] << -Delta
Sigma_orig['nambu'][2,7] << Delta
Sigma_orig['nambu'][3,5] << -Delta
Sigma_orig['nambu'][3,6] << Delta
Sigma_orig['nambu'][5,0] << Delta
Sigma_orig['nambu'][6,0] << -Delta
Sigma_orig['nambu'][4,1] << Delta
Sigma_orig['nambu'][7,1] << -Delta
Sigma_orig['nambu'][4,2] << -Delta
Sigma_orig['nambu'][7,2] << Delta
Sigma_orig['nambu'][5,3] << -Delta
Sigma_orig['nambu'][6,3] << Delta
def extract_Gloc(mu):
ret = Gloc.copy()
ret.zero()
Gk = ret.copy()
mu_mat = np.zeros((8,8))
for i in range(4):
mu_mat[i,i] = mu
mu_mat[i+4,i+4] = -mu
nk = Hk_nambu.shape[0]
ikarray = np.array(range(nk))
for ik in mpi.slice_array(ikarray):
Gk['nambu'] << inverse(iOmega_n - Hk_nambu[ik] + mu_mat - Sigma_orig['nambu'])
ret['nambu'] += Gk['nambu']
mpi.barrier()
ret['nambu'] << mpi.all_reduce(mpi.world, ret['nambu'], lambda x, y: x + y)/nk
return ret
def Dens(mu):
dens = 2*extract_Gloc(mu)['nambu'][:4,:4].total_density()
if abs(dens.imag) > 1e-20:
mpi.report("Warning: Imaginary part of density will be ignored ({})".format(str(abs(dens.imag))))
return dens.real
mu, density = dichotomy(Dens, mu, n0*4, prec_mu, .5, max_loops = 100, x_name="chemical potential", y_name="density", verbosity=3)
Gloc << extract_Gloc(mu)
nlat = 2*Gloc['nambu'][:4,:4].total_density().real #lattice density
if it == 1:
for i in range(4):
Sigma_orig['nambu'][i,i] << .5*U
Sigma_orig['nambu'][i+4,i+4] << -.5*U
G0_orig = Gloc.copy() # G0 in the original basis
G0_orig << inverse(Sigma_orig + inverse(Gloc))
G0_trans = G0_orig.copy() #G0 in the transformed basis
for i in range(len(G0_orig.mesh)):
G0_trans['nambu'].data[i,:,:] = Q.T.dot(G0_orig['nambu'].data[i,:,:]).dot(Q)
S.G0_iw['s+'][0,0] << G0_trans['nambu'][0,0]
S.G0_iw['s-'][0,0] << G0_trans['nambu'][1,1]
S.G0_iw['d+'][0,0] << G0_trans['nambu'][2,2]
S.G0_iw['d-'][0,0] << G0_trans['nambu'][3,3]
S.G0_iw['px'][:,:] << G0_trans['nambu'][4:6,4:6]
S.G0_iw['py'][:,:] << G0_trans['nambu'][6:8,6:8]
S.solve(h_int=h_int, **p)
Sigma_symm = S.Sigma_iw.copy() #symmetrized version of S.Sigma_iw
for name, s_iw in S.Sigma_iw:
Sigma_symm[name] = make_hermitian(s_iw)
symm = Sigma_symm['s+'].copy()
symm << .5*(Sigma_symm['s+'] - Sigma_symm['s-'].conjugate())
Sigma_symm['s+'] << symm
Sigma_symm['s-'] << -symm.conjugate()
symm << .5*(Sigma_symm['d+'] - Sigma_symm['d-'].conjugate())
Sigma_symm['d+'] << symm
Sigma_symm['d-'] << -symm.conjugate()
symm[0,0] << .25*(Sigma_symm['px'][0,0] - Sigma_symm['px'][1,1].conjugate() + Sigma_symm['py'][0,0] - Sigma_symm['py'][1,1].conjugate())
Sigma_symm['px'][0,0] << symm[0,0]
Sigma_symm['px'][1,1] << -symm.conjugate()[0,0]
Sigma_symm['py'][0,0] << symm[0,0]
Sigma_symm['py'][1,1] << -symm.conjugate()[0,0]
symm[0,0] << .25*(Sigma_symm['px'][0,1].real + Sigma_symm['px'][1,0].real - Sigma_symm['py'][0,1].real - Sigma_symm['py'][1,0].real)
Sigma_symm['px'][0,1] << symm[0,0]
Sigma_symm['px'][1,0] << symm[0,0]
Sigma_symm['py'][0,1] << -symm[0,0]
Sigma_symm['py'][1,0] << -symm[0,0]
Sigma_trans = Sigma_orig.copy()
Sigma_trans.zero()
Sigma_trans['nambu'][0,0] << Sigma_symm['s+'][0,0]
Sigma_trans['nambu'][1,1] << Sigma_symm['s-'][0,0]
Sigma_trans['nambu'][2,2] << Sigma_symm['d+'][0,0]
Sigma_trans['nambu'][3,3] << Sigma_symm['d-'][0,0]
Sigma_trans['nambu'][4:6,4:6] << Sigma_symm['px'][:,:]
Sigma_trans['nambu'][6:8,6:8] << Sigma_symm['py'][:,:]
for i in range(len(G0_orig.mesh)):
Sigma_orig['nambu'].data[i,:,:] = Q.dot(Sigma_trans['nambu'].data[i,:,:]).dot(Q.T)
G_symm = S.G_iw.copy()
G_symm << inverse(inverse(S.G0_iw) - Sigma_symm)
G_trans = Sigma_trans.copy()
G_trans.zero()
G_trans['nambu'][0,0] << G_symm['s+'][0,0]
G_trans['nambu'][1,1] << G_symm['s-'][0,0]
G_trans['nambu'][2,2] << G_symm['d+'][0,0]
G_trans['nambu'][3,3] << G_symm['d-'][0,0]
G_trans['nambu'][4:6,4:6] << G_symm['px'][:,:]
G_trans['nambu'][6:8,6:8] << G_symm['py'][:,:]
G_orig = G_trans.copy()
for i in range(len(G0_orig.mesh)):
G_orig['nambu'].data[i,:,:] = Q.dot(G_trans['nambu'].data[i,:,:]).dot(Q.T)
nimp = 2*G_orig['nambu'][:4,:4].total_density().real #impurity density
dG = G_orig.copy()
dG << G_orig - Gloc
maxabs = np.abs(dG['nambu'].data).max()
#save the last iteration some things from each iteration to check for convergence
if mpi.is_master_node():
ar = HDFArchive(outfile+'.h5','a')
ar['iterations'] = it
ar['G0_solver'] = S.G0_iw
ar['G_tau_solver'] = S.G_tau
ar['G_orig'] = G_orig
ar['G_solver'] = S.G_iw
ar['Sigma_solver'] = S.Sigma_iw
ar['Sigma_orig'] = Sigma_orig
ar['Sigma_orig_00-%d'%it] = Sigma_orig['nambu'][0,0]
ar['Sigma_orig_01-%d'%it] = Sigma_orig['nambu'][0,1]
ar['Sigma_orig_03-%d'%it] = Sigma_orig['nambu'][0,3]
ar['Sigma_orig_05-%d'%it] = Sigma_orig['nambu'][0,5]
ar['nimp-%d'%it] = nimp
ar['nlat-%d'%it] = nlat
ar['mu-%d'%it] = mu
ar['maxabs-%d'%it] = maxabs
del ar
#save everything from every iteration to a separate larger file for debugging
if mpi.is_master_node():
ar = HDFArchive(outfile+'_iterations.h5','a')
ar['iterations'] = it
ar['Solver-%d'%it] = S
ar['Sigma_orig-%d'%it] = Sigma_orig
ar['Sigma_solver-%d'%it] = S.Sigma_iw
ar['Sigma_symm-%d'%it] = Sigma_symm
ar['Sigma_trans-%d'%it] = Sigma_trans
ar['G0_orig-%d'%it] = G0_orig
ar['G0_solver-%d'%it] = S.G0_iw
ar['mu-%d'%it] = mu
ar['maxabs-%d'%it] = maxabs
del ar