mirror of
https://github.com/triqs/dft_tools
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449 lines
19 KiB
Python
449 lines
19 KiB
Python
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################################################################################
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#
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# TRIQS: a Toolbox for Research in Interacting Quantum Systems
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#
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# Copyright (C) 2011 by M. Aichhorn, L. Pourovskii, V. Vildosola
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#
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# TRIQS is free software: you can redistribute it and/or modify it under the
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# terms of the GNU General Public License as published by the Free Software
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# Foundation, either version 3 of the License, or (at your option) any later
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# version.
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#
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# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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# details.
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#
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# You should have received a copy of the GNU General Public License along with
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# TRIQS. If not, see <http://www.gnu.org/licenses/>.
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#
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################################################################################
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from pytriqs.operators import *
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from pytriqs.applications.impurity_solvers.cthyb_matrix import Solver
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from pytriqs.applications.dft.U_matrix import *
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import pytriqs.utility.mpi as mpi
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from types import *
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import numpy
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def sum_list(L):
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""" Can sum any list"""
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return reduce(lambda x, y: x+y, L) if len(L)>0 else []
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#########################################
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#
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# Solver for the Multi-Band problem
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#
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#########################################
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class SolverMultiBand(Solver):
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"""
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This is a general solver for a multiband local Hamiltonian.
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Calling arguments:
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beta = inverse temperature
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n_orb = Number of local orbitals
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U_interact = Average Coulomb interaction
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J_hund = Hund coupling
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use_spinflip = true/false
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use_pairhop = true/false
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use_matrix: Use the interaction matrix calculated from the Slater integrals
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is use_matrix, you need also:
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l: angular momentum of the orbital, l=2 is d
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T: Transformation matrix for U vertex. If not present, use standard complex harmonics
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"""
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def __init__(self, beta, n_orb, gf_struct = False, map = False):
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self.n_orb = n_orb
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# either get or construct gf_struct
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if (gf_struct):
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assert map, "give also the mapping!"
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self.map = map
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else:
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# standard gf_struct and map
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gf_struct = [ ('%s'%(ud),[n for n in range(n_orb)]) for ud in ['up','down'] ]
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self.map = {'up' : ['up' for v in range(n_orb)], 'down' : ['down' for v in range(n_orb)]}
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# now initialize the solver with the stuff given above:
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Solver.__init__(self, beta = beta, gf_struct = gf_struct)
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def solve(self, U_interact=None, J_hund=None, use_spinflip=False,
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use_matrix = True, l=2, T=None, dim_reps=None, irep=None, deg_orbs = [], sl_int = None, **params):
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self.use_spinflip = use_spinflip
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self.U, self.Up, self.U4ind, self.offset = set_U_matrix(U_interact,J_hund,self.n_orb,l,use_matrix,T,sl_int,use_spinflip,dim_reps,irep)
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# define mapping of indices:
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self.map_ind={}
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for nm in self.map:
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bl_names = self.map[nm]
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block = []
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for a,al in self.gf_struct:
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if a in bl_names: block.append(al)
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self.map_ind[nm] = range(self.n_orb)
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i = 0
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for al in block:
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cnt = 0
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for a in range(len(al)):
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self.map_ind[nm][i] = cnt
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i = i+1
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cnt = cnt+1
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# set the Hamiltonian
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if (use_spinflip==False):
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Hamiltonian = self.__set_hamiltonian_density()
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else:
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if (use_matrix):
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#Hamiltonian = self.__set_full_hamiltonian_slater()
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Hamiltonian = self.__set_spinflip_hamiltonian_slater()
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else:
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Hamiltonian = self.__set_full_hamiltonian_kanamori(J_hund = J_hund)
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# set the Quantum numbers
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Quantum_Numbers = self.__set_quantum_numbers(self.gf_struct)
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# Determine if there are only blocs of size 1:
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self.blocssizeone = True
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for ib in self.gf_struct:
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if (len(ib[1])>1): self.blocssizeone = False
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nc = params.pop("n_cycles",10000)
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if ((self.blocssizeone) and (self.use_spinflip==False)):
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use_seg = True
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else:
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use_seg = False
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#gm = self.set_global_moves(deg_orbs)
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Solver.solve(self,H_local = Hamiltonian, quantum_numbers = Quantum_Numbers, n_cycles = nc, use_segment_picture = use_seg, **params)
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def set_global_moves(self, deg_orbs, factor=0.05):
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# Sets some global moves given orbital degeneracies:
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strbl = ''
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strind = ''
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inddone = []
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for orbs in deg_orbs:
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ln = len(orbs)
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orbsorted = sorted(orbs)
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for ii in range(ln):
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if (strbl!=''): strbl += ','
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bl1 = orbsorted[ii]
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bl2 = orbsorted[(ii+1)%ln]
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ind1 = [ll for ll in self.Sigma[bl1].indices ]
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ind2 = [ll for ll in self.Sigma[bl2].indices ]
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strbl += "'" + bl1 + "':'" + bl2 + "'"
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for kk, ind in enumerate(ind1):
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if not (ind in inddone):
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if (strind!=''): strind += ','
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strind += '%s:%s'%(ind1[kk],ind2[kk])
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inddone.append(ind)
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if len(deg_orbs)>0:
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str = 'Global_Moves = [ (%s, lambda (a,alpha,dag) : ({ '%factor + strbl + ' }[a], {' + strind + '}[alpha], dag) )]'
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exec str
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return Global_Moves
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else:
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return []
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def __set_hamiltonian_density(self):
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# density-density Hamiltonian:
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spinblocs = [v for v in self.map]
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#print spinblocs
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Hamiltonian = N(self.map[spinblocs[0]][0],0) # initialize it
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for sp1 in spinblocs:
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for sp2 in spinblocs:
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for i in range(self.n_orb):
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for j in range(self.n_orb):
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if (sp1==sp2):
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Hamiltonian += 0.5 * self.U[self.offset+i,self.offset+j] * N(self.map[sp1][i],self.map_ind[sp1][i]) * N(self.map[sp2][j],self.map_ind[sp2][j])
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else:
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Hamiltonian += 0.5 * self.Up[self.offset+i,self.offset+j] * N(self.map[sp1][i],self.map_ind[sp1][i]) * N(self.map[sp2][j],self.map_ind[sp2][j])
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Hamiltonian -= N(self.map[spinblocs[0]][0],0) # substract the initializing value
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return Hamiltonian
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def __set_full_hamiltonian_slater(self):
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spinblocs = [v for v in self.map]
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Hamiltonian = N(self.map[spinblocs[0]][0],0) # initialize it
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#print "Starting..."
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# use the full 4-index U-matrix:
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#for sp1 in spinblocs:
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# for sp2 in spinblocs:
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for m1 in range(self.n_orb):
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for m2 in range(self.n_orb):
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for m3 in range(self.n_orb):
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for m4 in range(self.n_orb):
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if (abs(self.U4ind[self.offset+m1,self.offset+m2,self.offset+m3,self.offset+m4])>0.00001):
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for sp1 in spinblocs:
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for sp2 in spinblocs:
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#print sp1,sp2,m1,m2,m3,m4
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Hamiltonian += 0.5 * self.U4ind[self.offset+m1,self.offset+m2,self.offset+m3,self.offset+m4] * \
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Cdag(self.map[sp1][m1],self.map_ind[sp1][m1]) * Cdag(self.map[sp2][m2],self.map_ind[sp2][m2]) * C(self.map[sp2][m4],self.map_ind[sp2][m4]) * C(self.map[sp1][m3],self.map_ind[sp1][m3])
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#print "end..."
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Hamiltonian -= N(self.map[spinblocs[0]][0],0) # substract the initializing value
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return Hamiltonian
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def __set_spinflip_hamiltonian_slater(self):
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"""Takes only spin-flip and pair-hopping terms"""
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spinblocs = [v for v in self.map]
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Hamiltonian = N(self.map[spinblocs[0]][0],0) # initialize it
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#print "Starting..."
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# use the full 4-index U-matrix:
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#for sp1 in spinblocs:
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# for sp2 in spinblocs:
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for m1 in range(self.n_orb):
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for m2 in range(self.n_orb):
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for m3 in range(self.n_orb):
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for m4 in range(self.n_orb):
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if ((abs(self.U4ind[self.offset+m1,self.offset+m2,self.offset+m3,self.offset+m4])>0.00001) and
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( ((m1==m2)and(m3==m4)) or ((m1==m3)and(m2==m4)) or ((m1==m4)and(m2==m3)) ) ):
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for sp1 in spinblocs:
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for sp2 in spinblocs:
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#print sp1,sp2,m1,m2,m3,m4
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Hamiltonian += 0.5 * self.U4ind[self.offset+m1,self.offset+m2,self.offset+m3,self.offset+m4] * \
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Cdag(self.map[sp1][m1],self.map_ind[sp1][m1]) * Cdag(self.map[sp2][m2],self.map_ind[sp2][m2]) * C(self.map[sp2][m4],self.map_ind[sp2][m4]) * C(self.map[sp1][m3],self.map_ind[sp1][m3])
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#print "end..."
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Hamiltonian -= N(self.map[spinblocs[0]][0],0) # substract the initializing value
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return Hamiltonian
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def __set_full_hamiltonian_kanamori(self,J_hund):
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spinblocs = [v for v in self.map]
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assert len(spinblocs)==2,"spinflips in Kanamori representation only implemented for up/down structure!"
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Hamiltonian = N(self.map[spinblocs[0]][0],0) # initialize it
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# density terms:
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for sp1 in spinblocs:
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for sp2 in spinblocs:
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for i in range(self.n_orb):
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for j in range(self.n_orb):
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if (sp1==sp2):
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Hamiltonian += 0.5 * self.U[self.offset+i,self.offset+j] * N(self.map[sp1][i],self.map_ind[sp1][i]) * N(self.map[sp2][j],self.map_ind[sp2][j])
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else:
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Hamiltonian += 0.5 * self.Up[self.offset+i,self.offset+j] * N(self.map[sp1][i],self.map_ind[sp1][i]) * N(self.map[sp2][j],self.map_ind[sp2][j])
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# spinflip term:
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sp1 = spinblocs[0]
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sp2 = spinblocs[1]
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for i in range(self.n_orb-1):
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for j in range(i+1,self.n_orb):
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Hamiltonian -= J_hund * ( Cdag(self.map[sp1][i],self.map_ind[sp1][i]) * C(self.map[sp2][i],self.map_ind[sp2][i]) * Cdag(self.map[sp2][j],self.map_ind[sp2][j]) * C(self.map[sp1][j],self.map_ind[sp1][j]) ) # first term
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Hamiltonian -= J_hund * ( Cdag(self.map[sp2][i],self.map_ind[sp2][i]) * C(self.map[sp1][i],self.map_ind[sp1][i]) * Cdag(self.map[sp1][j],self.map_ind[sp1][j]) * C(self.map[sp2][j],self.map_ind[sp2][j]) ) # second term
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# pairhop terms:
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for i in range(self.n_orb-1):
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for j in range(i+1,self.n_orb):
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Hamiltonian -= J_hund * ( Cdag(self.map[sp1][i],self.map_ind[sp1][i]) * Cdag(self.map[sp2][i],self.map_ind[sp2][i]) * C(self.map[sp1][j],self.map_ind[sp1][j]) * C(self.map[sp2][j],self.map_ind[sp2][j]) ) # first term
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Hamiltonian -= J_hund * ( Cdag(self.map[sp2][j],self.map_ind[sp2][j]) * Cdag(self.map[sp1][j],self.map_ind[sp1][j]) * C(self.map[sp2][i],self.map_ind[sp2][i]) * C(self.map[sp1][i],self.map_ind[sp1][i]) ) # second term
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Hamiltonian -= N(self.map[spinblocs[0]][0],0) # substract the initializing value
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return Hamiltonian
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def __set_quantum_numbers(self,gf_struct):
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QN = {}
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spinblocs = [v for v in self.map]
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# Define the quantum numbers:
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if (self.use_spinflip) :
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Ntot = sum_list( [ N(self.map[s][i],self.map_ind[s][i]) for s in spinblocs for i in range(self.n_orb) ] )
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QN['NtotQN'] = Ntot
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#QN['Ntot'] = sum_list( [ N(self.map[s][i],i) for s in spinblocs for i in range(self.n_orb) ] )
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if (len(spinblocs)==2):
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# Assuming up/down structure:
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Sz = sum_list( [ N(self.map[spinblocs[0]][i],self.map_ind[spinblocs[0]][i])-N(self.map[spinblocs[1]][i],self.map_ind[spinblocs[1]][i]) for i in range(self.n_orb) ] )
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QN['SzQN'] = Sz
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# new quantum number: works only if there are only spin-flip and pair hopping, not any more complicated things
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for i in range(self.n_orb):
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QN['Sz2_%s'%i] = (N(self.map[spinblocs[0]][i],self.map_ind[spinblocs[0]][i])-N(self.map[spinblocs[1]][i],self.map_ind[spinblocs[1]][i])) * (N(self.map[spinblocs[0]][i],self.map_ind[spinblocs[0]][i])-N(self.map[spinblocs[1]][i],self.map_ind[spinblocs[1]][i]))
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else :
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for ibl in range(len(gf_struct)):
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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])) ] )
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return QN
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def fit_tails(self):
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"""Fits the tails using the constant value for the Re Sigma calculated from F=Sigma*G.
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Works only for blocks of size one."""
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#if (len(self.gf_struct)==2*self.n_orb):
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if (self.blocssizeone):
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spinblocs = [v for v in self.map]
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mpi.report("Fitting tails manually")
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known_coeff = numpy.zeros([1,1,2],numpy.float_)
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msh = [x.imag for x in self.G[self.map[spinblocs[0]][0]].mesh ]
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fit_start = msh[self.fitting_Frequency_Start]
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fit_stop = msh[self.N_Frequencies_Accumulated]
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# Fit the tail of G just to get the density
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for n,g in self.G:
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g.fitTail([[[0,0,1]]],7,fit_start,2*fit_stop)
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densmat = self.G.density()
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for sig1 in spinblocs:
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for i in range(self.n_orb):
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coeff = 0.0
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for sig2 in spinblocs:
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for j in range(self.n_orb):
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if (sig1==sig2):
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coeff += self.U[self.offset+i,self.offset+j] * densmat[self.map[sig1][j]][0,0].real
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else:
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coeff += self.Up[self.offset+i,self.offset+j] * densmat[self.map[sig2][j]][0,0].real
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known_coeff[0,0,1] = coeff
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self.Sigma[self.map[sig1][i]].fitTail(fixed_coef = known_coeff, order_max = 3, fit_start = fit_start, fit_stop = fit_stop)
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else:
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for n,sig in self.Sigma:
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known_coeff = numpy.zeros([sig.N1,sig.N2,1],numpy.float_)
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msh = [x.imag for x in sig.mesh]
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fit_start = msh[self.fitting_Frequency_Start]
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fit_stop = msh[self.N_Frequencies_Accumulated]
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sig.fitTail(fixed_coef = known_coeff, order_max = 3, fit_start = fit_start, fit_stop = fit_stop)
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class SolverMultiBandOld(SolverMultiBand):
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"""
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Old MultiBand Solver construct
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"""
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def __init__(self, Beta, Norb, U_interact=None, J_Hund=None, GFStruct=False, map=False, use_spinflip=False,
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useMatrix = True, l=2, T=None, dimreps=None, irep=None, deg_orbs = [], Sl_Int = None):
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SolverMultiBand.__init__(self, beta=Beta, n_orb=Norb, gf_struct=GFStruct, map=map)
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self.U_interact = U_interact
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self.J_Hund = J_Hund
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self.use_spinflip = use_spinflip
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self.useMatrix = useMatrix
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self.l = l
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self.T = T
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self.dimreps = dimreps
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self.irep = irep
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self.deg_orbs = deg_orbs
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self.Sl_Int = Sl_Int
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self.gen_keys = copy.deepcopy(self.__dict__)
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msg = """
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**********************************************************************************
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Warning: You are using the old constructor for the solver. Beware that this will
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be deprecated in future versions. Please check the documentation.
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**********************************************************************************
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"""
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mpi.report(msg)
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def Solve(self):
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params = copy.deepcopy(self.__dict__)
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for i in self.gen_keys: self.params.pop(i)
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self.params.pop("gen_keys")
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self.solve(self, U_interact=self.U_interact, J_hund=self.J_Hund, use_spinflip=self.use_spinflip,
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use_matrix = self.useMatrix, l=self.l, T=self.T, dim_reps=self.dimreps, irep=self.irep,
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deg_orbs = self.deg_orbs, sl_int = self.Sl_Int, **params)
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def set_U_matrix(U_interact,J_hund,n_orb,l,use_matrix=True,T=None,sl_int=None,use_spinflip=False,dim_reps=None,irep=None):
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""" Set up the interaction vertex"""
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offset = 0
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U4ind = None
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U = None
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Up = None
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if (use_matrix):
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if not (sl_int is None):
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Umat = Umatrix(l=l)
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assert len(sl_int)==(l+1),"sl_int has the wrong length"
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if (type(sl_int)==ListType):
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Rcl = numpy.array(sl_int)
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else:
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Rcl = sl_int
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Umat(T=T,Rcl=Rcl)
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else:
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if ((U_interact==None)and(J_hund==None)):
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mpi.report("Give U,J or Slater integrals!!!")
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assert 0
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Umat = Umatrix(U_interact=U_interact, J_hund=J_hund, l=l)
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Umat(T=T)
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|
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Umat.reduce_matrix()
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if (Umat.N==Umat.Nmat):
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# Transformation T is of size 2l+1
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U = Umat.U
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Up = Umat.Up
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else:
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# Transformation is of size 2(2l+1)
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U = Umat.U
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# now we have the reduced matrices U and Up, we need it for tail fitting anyways
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|
|
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if (use_spinflip):
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#Take the 4index Umatrix
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# check for imaginary matrix elements:
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if (abs(Umat.Ufull.imag)>0.0001).any():
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mpi.report("WARNING: complex interaction matrix!! Ignoring imaginary part for the moment!")
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mpi.report("If you want to change this, look into Wien2k/solver_multiband.py")
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U4ind = Umat.Ufull.real
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|
|
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# this will be changed for arbitrary irep:
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|
# use only one subgroup of orbitals?
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if not (irep is None):
|
|
#print irep, dim_reps
|
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assert not (dim_reps is None), "Dimensions of the representatives are missing!"
|
|
assert n_orb==dim_reps[irep-1],"Dimensions of dimrep and n_orb do not fit!"
|
|
for ii in range(irep-1):
|
|
offset += dim_reps[ii]
|
|
else:
|
|
if ((U_interact==None)and(J_hund==None)):
|
|
mpi.report("For Kanamori representation, give U and J!!")
|
|
assert 0
|
|
U = numpy.zeros([n_orb,n_orb],numpy.float_)
|
|
Up = numpy.zeros([n_orb,n_orb],numpy.float_)
|
|
for i in range(n_orb):
|
|
for j in range(n_orb):
|
|
if (i==j):
|
|
Up[i,i] = U_interact
|
|
else:
|
|
Up[i,j] = U_interact - 2.0*J_hund
|
|
U[i,j] = U_interact - 3.0*J_hund
|
|
|
|
return U, Up, U4ind, offset
|