def Transform_RealSpace_to_SymmetryBasis(self,IN, OUT = None):
""" IN[i,j] in real space --> OUT into the symmetry basis"""
OUT = OUT if OUT else BlockGf(G)
for sig,B in IN:
for k,ind in enumerate(['+1-', '-1-','+i-', '-i-']) :
OUT[ind+sig] = sum_list ( [ sum_list ( [ B[i+1,j+1]* self.P[j,k] * self.Pinv[k,i] for j in range(4) ] ) for i in range(4) ] )
return OUT
def __init__(self,Beta,Norb,U_interact,J_Hund) :
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
Hamiltonian = U_interact * sum_list( [ N('up',i)*N('down',i) for i in range(Norb) ] )
for i in range(Norb-1):
for j in range(i+1,Norb):
Hamiltonian += (U_interact-2*J_Hund) * ( N('up',i) * N('down',j) +
N('down',i) * N('up',j) ) + \
(U_interact-3*J_Hund) * ( N('up',i) * N('up',j) +
N('down',i) * N('down',j) )
#Quantum_Numbers = {}
#for i in range(Norb):
# Quantum_Numbers['N%sup'%(i+1)] = N('up',i)
# Quantum_Numbers['N%sdown'%(i+1)] = N('down',i)
Ntot = sum_list( [ N(s,i) for s in ['up','down'] for i in range(Norb) ] )
Sz = sum_list( [ N('up',i)-N('down',i) for i in range(Norb) ] )
Quantum_Numbers = {'Ntot' : Ntot, 'Sz' : Sz}
Solver.__init__(self,
Beta = Beta,
GFstruct = [ ('%s'%(ud),[n for n in range(Norb)]) for ud in ['up','down'] ],
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers )
self.N_Cycles = 10000
def __init__(self,Beta,U_interact) :
self.P = numpy.array([[1,1,1,1], [1,-1,1,-1],[1,1,-1,-1],[1,-1,-1,1]])/2.
self.Pinv = numpy.linalg.inv(self.P)
def Cdiag(s):
s= '-%s'%s
return [ C('00'+s,1), C('10'+s,1), C('01'+s,1),C('11'+s,1) ]
Cnat,Nnat={},{}
for i in range(4) :
s= 'up-%d'%(i+1)
Cnat[s] = sum_list( [ self.P[i,j]*c for j,c in enumerate(Cdiag('up'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
s= 'down-%d'%(i+1)
Cnat[s] = sum_list( [ self.P[i,j]*c for j,c in enumerate(Cdiag('down'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
def symm(s):
s= '-%s'%s
Cdag('00'+s,1).symmetry()['kx'] = 1
Cdag('10'+s,1).symmetry()['kx'] = -1
Cdag('01'+s,1).symmetry()['kx'] = 1
Cdag('11'+s,1).symmetry()['kx'] = -1
Cdag('00'+s,1).symmetry()['ky'] = 1
Cdag('10'+s,1).symmetry()['ky'] = 1
Cdag('01'+s,1).symmetry()['ky'] = -1
Cdag('11'+s,1).symmetry()['ky'] = -1
symm('up'); symm('down')
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
Hamiltonian = U_interact* sum_list( [ Nnat['up-%d'%(i+1)]* Nnat['down-%d'%(i+1)] for i in range (4)])
N_u = sum_list( [ Nnat['up-%d'%(i+1)] for i in range(4) ] )
N_d = sum_list( [ Nnat['down-%d'%(i+1)] for i in range(4) ] )
Quantum_Numbers = { 'kx' : 'kx', 'ky' : 'ky', 'N_u' : N_u, 'N_d' : N_d }
Solver.__init__(self,
Beta = Beta,
GFstruct = [ ('00-up',[1]), ('10-up',[1]), ('01-up',[1]), ('11-up',[1]),
('00-down',[1]), ('10-down',[1]), ('01-down',[1]), ('11-down',[1]) ],
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers,
Nmax = 2000)
self.N_Cycles = 100000
self.N_Frequencies_Accumulated = 4*int(0.075*Beta/(2*3.1415))
self.fitting_Frequency_Start = 3*int(0.075*Beta/(2*3.1415))
self.Length_Cycle = 100
self.Nmax_Matrix = 200
self.Use_Segment_Picture = False
def Transform_SymmetryBasis_toRealSpace(self,IN, OUT = None):
""" IN : in symmetry cluster indices. Returns OUT to real space"""
OUT = OUT if OUT else BlockGf(G)
for sig,B in OUT :
for i in range(4):
for j in range(4):
B[i+1,j+1] = sum_list( [ self.P[i,k]* self.Pinv[k,j]* IN[ind+sig]
for k,ind in enumerate(['+1-', '-1-','+i-', '-i-']) ])
return OUT
def __init__(self,Beta,U_interact) :
self.P = numpy.array([[1,1,1,1], [1,-1,1,-1],[1,1,-1,-1],[1,-1,-1,1]])/2.
self.Pinv = numpy.linalg.inv(self.P)
def Cdiag(s):
s= '-%s'%s
return [ C('00'+s,1), C('10'+s,1), C('01'+s,1),C('11'+s,1) ]
Cnat,Nnat={},{}
for i in range(4) :
s= 'up-%d'%(i+1)
Cnat[s] = sum_list( [ self.P[i,j]*c for j,c in enumerate(Cdiag('up'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
s= 'down-%d'%(i+1)
Cnat[s] = sum_list( [ self.P[i,j]*c for j,c in enumerate(Cdiag('down'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
def symm(s):
s= '-%s'%s
Cdag('00'+s,1).symmetry()['kx'] = 1
Cdag('10'+s,1).symmetry()['kx'] = -1
Cdag('01'+s,1).symmetry()['kx'] = 1
Cdag('11'+s,1).symmetry()['kx'] = -1
Cdag('00'+s,1).symmetry()['ky'] = 1
Cdag('10'+s,1).symmetry()['ky'] = 1
Cdag('01'+s,1).symmetry()['ky'] = -1
Cdag('11'+s,1).symmetry()['ky'] = -1
symm('up'); symm('down')
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
Hamiltonian = U_interact* sum_list( [ Nnat['up-%d'%(i+1)]* Nnat['down-%d'%(i+1)] for i in range (4)]) #!!
N_u = sum_list( [ Nnat['up-%d'%(i+1)] for i in range(4) ] )
N_d = sum_list( [ Nnat['down-%d'%(i+1)] for i in range(4) ] )
Quantum_Numbers = { 'kx' : 'kx', 'ky' : 'ky', 'N_u' : N_u, 'N_d' : N_d }
Solver.__init__(self,Beta=Beta,GFstruct=[ ('00-up',[1]), ('10-up',[1]), ('01-up',[1]), ('11-up',[1]),
('00-down',[1]), ('10-down',[1]), ('01-down',[1]), ('11-down',[1]) ],
H_Local = Hamiltonian,Quantum_Numbers= Quantum_Numbers )
self.N_Cycles = 10
def __set_quantum_numbers(self,gf_struct):
QN = {}
spinblocs = [v for v in self.map]
# Define the quantum numbers:
if (self.use_spinflip) :
Ntot = sum_list( [ N(self.map[s][i],i) for s in spinblocs for i in range(self.n_orb) ] )
QN['NtotQN'] = Ntot
#QN['Ntot'] = sum_list( [ N(self.map[s][i],i) for s in spinblocs for i in range(self.n_orb) ] )
if (len(spinblocs)==2):
# Assuming up/down structure:
Sz = sum_list( [ N(self.map[spinblocs[0]][i],i)-N(self.map[spinblocs[1]][i],i) for i in range(self.n_orb) ] )
QN['SzQN'] = Sz
# new quantum number: works only if there are only spin-flip and pair hopping, not any more complicated things
for i in range(self.n_orb):
QN['Sz2_%s'%i] = (N(self.map[spinblocs[0]][i],i)-N(self.map[spinblocs[1]][i],i)) * (N(self.map[spinblocs[0]][i],i)-N(self.map[spinblocs[1]][i],i))
else :
for ibl in range(len(gf_struct)):
QN['N%s'%gf_struct[ibl][0]] = sum_list( [ N(gf_struct[ibl][0],gf_struct[ibl][1][i]) for i in range(len(gf_struct[ibl][1])) ] )
return QN