mirror of
https://github.com/triqs/dft_tools
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336 lines
12 KiB
Python
336 lines
12 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. Ferrero, O. Parcollet
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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 types import *
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#from pytriqs.applications.dft.U_matrix import *
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from U_matrix import *
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from pytriqs.gf.local import *
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#from hubbard_I import gf_hi_fullu, sigma_atomic_fullu
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import pytriqs.utility.mpi as mpi
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from itertools import izip
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import numpy
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import copy
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class Solver:
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"""
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Hartree-Fock Solver
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"""
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# initialisation:
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def __init__(self, beta, l, n_msb=1025, use_spin_orbit=False, Nmoments=5, dudarev=False):
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self.name = "Hartree-Fock"
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self.beta = beta
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self.l = l
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self.Nmsb = n_msb
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self.UseSpinOrbit = use_spin_orbit
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self.Converged = False
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self.Nspin = 2
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self.Nmoments=Nmoments
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self.dudarev = dudarev
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assert use_spin_orbit == False, "Spin-orbit is not implemented"
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self.Nlm = 2*l+1
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if (use_spin_orbit):
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# no blocks!
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self.gf_struct = [ ('ud', range(2*self.Nlm)) ]
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else:
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# up/down blocks:
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self.gf_struct = [ ('up', range(self.Nlm)), ('down', range(self.Nlm)) ]
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# construct Greens functions:
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self.a_list = [a for a,al in self.gf_struct]
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glist = lambda : [ GfImFreq(indices = al, beta = self.beta, n_points = self.Nmsb) for a,al in self.gf_struct]
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self.G = BlockGf(name_list = self.a_list, block_list = glist(),make_copies=False)
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self.G_Old = self.G.copy()
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self.G0 = self.G.copy()
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self.Sigma = self.G.copy()
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self.Sigma_Old = self.G.copy()
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def solve(self, U_int, J_hund, T=None, verbosity=0, Iteration_Number=1, Test_Convergence=0.0001):
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"""Calculation of the impurity Greens function using Hubbard-I"""
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if self.Converged :
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mpi.report("Solver %(name)s has already converged: SKIPPING"%self.__dict__)
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return
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if mpi.is_master_node():
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self.verbosity = verbosity
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else:
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self.verbosity = 0
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#self.Nmoments = 5
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ur,ujmn,umn=self.__set_umatrix(U=U_int,J=J_hund,T=T)
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M = [x for x in self.G.mesh]
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self.zmsb = numpy.array([x for x in M],numpy.complex_)
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# # for the tails:
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# tailtempl={}
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# for sig,g in self.G:
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# tailtempl[sig] = copy.deepcopy(g.tail)
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# for i in range(9): tailtempl[sig][i] *= 0.0
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# self.__save_eal('eal.dat',Iteration_Number)
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# mpi.report( "Starting Fortran solver %(name)s"%self.__dict__)
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self.Sigma_Old <<= self.Sigma
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self.G_Old <<= self.G
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# # call the fortran solver:
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# temp = 1.0/self.beta
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# gf,tail,self.atocc,self.atmag = gf_hi_fullu(e0f=self.ealmat, ur=ur, umn=umn, ujmn=ujmn,
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# zmsb=self.zmsb, nmom=self.Nmoments, ns=self.Nspin, temp=temp, verbosity = self.verbosity)
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#self.sig = sigma_atomic_fullu(gf=self.gf,e0f=self.eal,zmsb=self.zmsb,ns=self.Nspin,nlm=self.Nlm)
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def print_matrix(m):
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for row in m:
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print ''.join(map("{0:12.7f}".format, row))
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# Hartree-Fock solver
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self.Sigma.zero()
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dm = self.G.density()
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if mpi.is_master_node():
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# print
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# print " Reduced U-matrix:"
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# print " U:"
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# print_matrix(ujmn)
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# print " Up:"
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# print_matrix(umn)
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#
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## sig_test = {bl: numpy.zeros((self.Nlm, self.Nlm)) for bl in dm}
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# sig_test = {}
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# sig_test['up'] = numpy.dot(umn, dm['up'].real) + numpy.dot(ujmn, dm['down'].real)
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# sig_test['down'] = numpy.dot(umn, dm['down'].real) + numpy.dot(ujmn, dm['up'].real)
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# print " Sigma test:"
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# print_matrix(sig_test['up'])
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print
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print " Density matrix (up):"
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print_matrix(dm['up'])
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print
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print " Density matrix (down):"
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print_matrix(dm['down'])
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if self.dudarev:
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Ueff = U_int - J_hund
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corr_energy = 0.0
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dft_dc = 0.0
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for bl1 in dm:
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# (U - J) * (1/2 - n)
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self.Sigma[bl1] << Ueff * (0.5 * numpy.identity(self.Nlm) - dm[bl1])
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# 1/2 (U - J) * \sum_{\sig} [\sum_{m} n_{m,m \sig} - \sum_{m1,m2} n_{m1,m2 \sig} n_{m2,m1 \sig}]
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corr_energy += 0.5 * Ueff * (dm[bl1].trace() - (dm[bl1]*dm[bl1].conj()).sum()).real
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# V[n] * n^{\dagger}
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dft_dc += (self.Sigma[bl1](0) * dm[bl1].conj()).sum().real
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else:
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# !!!!!
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# !!!!! Mind the order of indices in the 4-index matrix!
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# !!!!!
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for il1 in xrange(self.Nlm):
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for il2 in xrange(self.Nlm):
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for il3 in xrange(self.Nlm):
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for il4 in xrange(self.Nlm):
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for bl1 in dm:
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for bl2 in dm:
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self.Sigma[bl1][il1, il2] += ur[il1, il3, il2, il4] * dm[bl2][il3, il4]
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if bl1 == bl2:
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self.Sigma[bl1][il1, il2] -= ur[il1, il3, il4, il2] * dm[bl1][il3, il4]
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if mpi.is_master_node() and self.verbosity > 0:
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print
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print " Sigma (up):"
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print_matrix(self.Sigma['up'](0).real)
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print
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print " Sigma (down):"
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print_matrix(self.Sigma['down'](0).real)
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# if (self.verbosity==0):
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# # No fortran output, so give basic results here
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# mpi.report("Atomic occupancy in Hubbard I Solver : %s"%self.atocc)
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# mpi.report("Atomic magn. mom. in Hubbard I Solver : %s"%self.atmag)
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# transfer the data to the GF class:
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if (self.UseSpinOrbit):
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nlmtot = self.Nlm*2 # only one block in this case!
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else:
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nlmtot = self.Nlm
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# M={}
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# isp=-1
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# for a,al in self.gf_struct:
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# isp+=1
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# M[a] = numpy.array(gf[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot,:]).transpose(2,0,1).copy()
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# for i in range(min(self.Nmoments,8)):
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# tailtempl[a][i+1] = tail[i][isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot]
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#
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# #glist = lambda : [ GfImFreq(indices = al, beta = self.beta, n_points = self.Nmsb, data =M[a], tail =self.tailtempl[a])
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# # for a,al in self.gf_struct]
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# glist = lambda : [ GfImFreq(indices = al, beta = self.beta, n_points = self.Nmsb) for a,al in self.gf_struct]
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# self.G = BlockGf(name_list = self.a_list, block_list = glist(),make_copies=False)
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#
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# self.__copy_Gf(self.G,M,tailtempl)
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#
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# # Self energy:
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# self.G0 <<= iOmega_n
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#
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# M = [ self.ealmat[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot] for isp in range((2*self.Nlm)/nlmtot) ]
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# self.G0 -= M
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# self.Sigma <<= self.G0 - inverse(self.G)
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#
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# # invert G0
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# self.G0.invert()
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def test_distance(G1,G2, dist) :
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def f(G1,G2) :
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#print abs(G1.data - G2.data)
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dS = max(abs(G1.data - G2.data).flatten())
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aS = max(abs(G1.data).flatten())
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if mpi.is_master_node():
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print " Distances:", dS, " vs ", aS * dist
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return dS <= aS*dist
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return reduce(lambda x,y : x and y, [f(g1,g2) for (i1,g1),(i2,g2) in izip(G1,G2)])
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mpi.report("\nChecking Sigma for convergence...\nUsing tolerance %s"%Test_Convergence)
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self.Converged = test_distance(self.Sigma,self.Sigma_Old,Test_Convergence)
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if self.Converged :
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mpi.report("Solver HAS CONVERGED")
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else :
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mpi.report("Solver has not yet converged")
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return corr_energy, dft_dc
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def GF_realomega(self, ommin, ommax, N_om, U_int, J_hund, T=None, verbosity=0, broadening=0.01):
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"""Calculates the GF and spectral function on the real axis."""
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delta_om = (ommax-ommin)/(1.0*(N_om-1))
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omega = numpy.zeros([N_om],numpy.complex_)
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ur,umn,ujmn=self.__set_umatrix(U=U_int,J=J_hund,T=T)
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for i in range(N_om):
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omega[i] = ommin + delta_om * i + 1j * broadening
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tailtempl={}
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for sig,g in self.G:
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tailtempl[sig] = copy.deepcopy(g.tail)
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for i in range(9): tailtempl[sig][i] *= 0.0
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temp = 1.0/self.beta
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gf,tail,self.atocc,self.atmag = gf_hi_fullu(e0f=self.ealmat, ur=ur, umn=umn, ujmn=ujmn,
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zmsb=omega, nmom=self.Nmoments, ns=self.Nspin, temp=temp, verbosity = verbosity)
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# transfer the data to the GF class:
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if (self.UseSpinOrbit):
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nlmtot = self.Nlm*2 # only one block in this case!
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else:
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nlmtot = self.Nlm
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M={}
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isp=-1
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for a,al in self.gf_struct:
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isp+=1
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M[a] = numpy.array(gf[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot,:]).transpose(2,0,1).copy()
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for i in range(min(self.Nmoments,8)):
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tailtempl[a][i+1] = tail[i][isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot]
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#glist = lambda : [ GfReFreq(indices = al, window = (ommin, ommax), n_points = N_om, data = M[a], tail = self.tailtempl[a])
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# for a,al in self.gf_struct] # Indices for the upfolded G
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glist = lambda : [ GfReFreq(indices = al, window = (ommin, ommax), n_points = N_om) for a,al in self.gf_struct]
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self.G = BlockGf(name_list = self.a_list, block_list = glist(),make_copies=False)
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self.__copy_Gf(self.G,M,tailtempl)
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# Self energy:
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self.G0 = self.G.copy()
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self.Sigma = self.G.copy()
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self.G0 <<= Omega + 1j*broadening
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M = [ self.ealmat[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot] for isp in range((2*self.Nlm)/nlmtot) ]
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self.G0 -= M
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self.Sigma <<= self.G0 - inverse(self.G)
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self.Sigma.note='ReFreq' # This is important for the put_Sigma routine!!!
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#sigmamat = sigma_atomic_fullu(gf=gf,e0f=self.ealmat,zmsb=omega,nlm=self.Nlm,ns=self.Nspin)
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#return omega,gf,sigmamat
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def __save_eal(self,Filename,it):
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f=open(Filename,'a')
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f.write('\neff. atomic levels, Iteration %s\n'%it)
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for i in range(self.Nlm*self.Nspin):
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for j in range(self.Nlm*self.Nspin):
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f.write("%10.6f %10.6f "%(self.ealmat[i,j].real,self.ealmat[i,j].imag))
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f.write("\n")
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f.close()
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def __copy_Gf(self,G,data,tail):
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""" Copies data and tail to Gf object GF """
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for s,g in G:
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g.data[:,:,:]=data[s][:,:,:]
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for imom in range(1,min(self.Nmoments,8)):
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g.tail.data[1+imom,:,:]=tail[s][imom]
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def set_atomic_levels(self,eal):
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""" Helps to set correctly the variables for the atomic levels from a dictionary."""
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assert (type(eal)==DictType), "Give a dictionary to set_atomic_levels!"
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cnt = 0
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self.ealmat[:,:] *= 0.0
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for ind in eal:
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self.Eff_Atomic_Levels[ind] = copy.deepcopy(eal[ind])
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if self.UseSpinOrbit:
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for ii in range(self.Nlm*2):
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for jj in range(self.Nlm*2):
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self.ealmat[ii,jj] = self.Eff_Atomic_Levels[ind][ii,jj]
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else:
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for ii in range(self.Nlm):
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for jj in range(self.Nlm):
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self.ealmat[cnt*self.Nlm + ii,cnt*self.Nlm + jj] = self.Eff_Atomic_Levels[ind][ii,jj]
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|
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cnt += 1
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def __set_umatrix(self,U,J,T=None):
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# U matrix:
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|
|
# l = (Nlm-1)/2
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# If T is specified, it is used to transform the Basis set
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Umat = U_matrix(l=self.l, U_int=U, J_hund=J, basis='cubic', T=T)
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|
|
U, Up = reduce_4index_to_2index(Umat)
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|
|
|
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|
|
return Umat, U, Up
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