mirror of https://github.com/triqs/dft_tools
293 lines
14 KiB
Fortran
293 lines
14 KiB
Fortran
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c ******************************************************************************
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c
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c TRIQS: a Toolbox for Research in Interacting Quantum Systems
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c
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c Copyright (C) 2011 by L. Pourovskii, V. Vildosola, C. Martins, M. Aichhorn
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c
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c TRIQS is free software: you can redistribute it and/or modify it under the
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c terms of the GNU General Public License as published by the Free Software
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c Foundation, either version 3 of the License, or (at your option) any later
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c version.
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c
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c TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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c WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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c FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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c details.
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c
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c You should have received a copy of the GNU General Public License along with
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c TRIQS. If not, see <http://www.gnu.org/licenses/>.
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c
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c *****************************************************************************/
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SUBROUTINE symmetrize_mat(Dmat,orbit,norbit)
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C %% %%
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C %% This subroutine applies the symmetry operations to the %%
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C %% density matrices stored in Dmat and puts the resulting %%
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C %% density matrices into the local coordinate system. %%
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C %% %%
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C %% This version can be used for SO computations. %%
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C %% %%
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C Definition of the variables :
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C ----------------------------
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USE common_data
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USE projections
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USE symm
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USE reps
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IMPLICIT NONE
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INTEGER :: norbit
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TYPE(matrix), DIMENSION(nsp,norbit) :: Dmat
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COMPLEX(KIND=8),DIMENSION(:,:,:,:), ALLOCATABLE :: sym_dmat
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COMPLEX(KIND=8),DIMENSION(:,:), ALLOCATABLE :: tmp_mat
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COMPLEX(KIND=8):: ephase
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TYPE(orbital), DIMENSION(norbit) :: orbit
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INTEGER :: isym, iorb, iatom, jorb, is, is1, l, i, m
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INTEGER :: isrt, jatom, imult, asym
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C
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C =========================================
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C Computation of the symmetrized matrices :
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C =========================================
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C
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iorb=1
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C Initialization of the iorb index.
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DO WHILE (iorb.lt.(norbit+1))
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C The use of the while-loop was motivated by the idea of studying
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C all the orbitals iorb associated to a same atomic sort isrt together.
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C At the end, the index iorb is incremented by nmult(isrt) so that the
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C following studied orbitals are associated to another atomic sort.
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l=orbit(iorb)%l
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isrt=orbit(iorb)%sort
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C
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C -----------------------------------------------------------------------------------
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C The s-orbitals are a particular case of a "non-mixing" basis and are treated here :
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C -----------------------------------------------------------------------------------
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IF (l==0) THEN
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C The table sym_dmat will store the symmetrized value of the density matrices of Dmat
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C associated to a same atomic sort isrt.
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ALLOCATE(sym_dmat(1,1,nsp,1:nmult(isrt)))
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sym_dmat=0.d0
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C Its size is nmult(isrt) because symmetry operations can transform the representants
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C of a same atomic sort one into another.
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C
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C Loop on the representants of the atomic sort isrt
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DO imult=0,nmult(isrt)-1
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iatom=orbit(iorb+imult)%atom
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C Loop on the symmetry operations of the system
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DO isym=1,nsym
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DO is=1,nsp
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ALLOCATE(tmp_mat(1,1))
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C If the calculation uses spin-polarized input files, the application of the symmetry operation
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C depends on the field srot%timeinv.
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IF(ifSP.AND.srot(isym)%timeinv) THEN
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C In this case (spin-polarized computation), the symmetry operation is block-diagonal in spin-space but
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C the time reversal operator is included.
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tmp_mat(1,1)=CONJG(Dmat(is,iorb+imult)%mat(1,1))
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C because of the antiunitarity of the operator, the conjugate of Dmat must be use
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ELSE
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tmp_mat(1,1)=Dmat(is,iorb+imult)%mat(1,1)
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ENDIF
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C
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C Definition of the index where the transformed Dmat will be stored. [jorb = R[isym](iorb)]
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jorb=srot(isym)%perm(iatom)-iatom+(imult+1)
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C
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C Computation of the phase factors in the case of a SO computation :
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C ------------------------------------------------------------------
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C For up/up and dn/dn blocks, no phase factor is needed.
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ephase=1.d0
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C For the up/dn block, initialisation of the phase factor
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IF(is==3) THEN
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ephase=EXP(CMPLX(0d0,srot(isym)%phase))
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C if srot%timeinv = .TRUE. , phase= g-a = 2pi+(alpha-gamma) and ephase = exp(+i(g-a)) = exp(+i(alpha-gamma))
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C if srot%timeinv = .FALSE., phase= a+g = 2pi-(alpha+gamma) and ephase = exp(+i(a+g)) = exp(-i(alpha+gamma))
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ENDIF
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C For the dn/up block, initialisation of the phase factor
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IF(is==4) THEN
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ephase=EXP(CMPLX(0d0,-srot(isym)%phase))
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C if srot%timeinv = .TRUE. , phase= g-a = 2pi+(alpha-gamma) and ephase = exp(-i(g-a)) = exp(-i(alpha-gamma))
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C if srot%timeinv = .FALSE., phase= a+g = 2pi-(alpha+gamma) and ephase = exp(-i(a+g)) = exp(+i(alpha+gamma))
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ENDIF
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C
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C Application of the symmetry operation which changes iorb in jorb=R[isym](iorb) :
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C --------------------------------------------------------------------------------
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C That's why the result is stored in the jorb section of sym_dmat.
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sym_dmat(1,1,is,jorb)=
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= sym_dmat(1,1,is,jorb)+tmp_mat(1,1)*ephase
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DEALLOCATE(tmp_mat)
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ENDDO ! End of the is loop
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ENDDO ! End of the isym loop
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ENDDO ! End of the imult loop
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C
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C Renormalization of the symmetrized density matrices :
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C -----------------------------------------------------
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IF (nsym.gt.0) THEN
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DO imult=0,nmult(isrt)-1
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DO is=1,nsp
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Dmat(is,iorb+imult)%mat(1,1)=
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& sym_dmat(1,1,is,imult+1)/nsym
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ENDDO
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ENDDO
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ENDIF
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DEALLOCATE(sym_dmat)
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C Incrementation of the iorb index (for the while loop)
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iorb=iorb+nmult(isrt)
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C
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C -----------------------------------------------------------------------------------------------------
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C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) ) :
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C -----------------------------------------------------------------------------------------------------
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ELSEIF (reptrans(l,isrt)%ifmixing) THEN
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C The table sym_dmat will store the symmetrized value of the density matrices of Dmat
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C associated to a same atomic sort isrt.
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ALLOCATE(sym_dmat(1:2*(2*l+1),1:2*(2*l+1),1,1:nmult(isrt)))
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sym_dmat=0.d0
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C Its size is nmult(isrt) because symmetry operations can transform the representants
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C of a same atomic sort one into another.
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C
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C Loop on the representants of the atomic sort isrt
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DO imult=0,nmult(isrt)-1
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iatom=orbit(iorb+imult)%atom
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C Loop on the symmetry operations of the system
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DO isym=1,nsym
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ALLOCATE(tmp_mat(1:2*(2*l+1),1:2*(2*l+1)))
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C We use the complete spin-space representation, so no trick on indices is necessary.
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tmp_mat(1:2*(2*l+1),1:2*(2*l+1))=
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& Dmat(1,iorb+imult)%mat(1:2*(2*l+1),1:2*(2*l+1))
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C If the calculation is spin-polarized, the symmetry operator is antiunitary.
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IF(ifSP.AND.srot(isym)%timeinv) THEN
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tmp_mat(1:2*(2*l+1),1:2*(2*l+1))=
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& CONJG(tmp_mat(1:2*(2*l+1),1:2*(2*l+1)))
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ENDIF
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C Definition of the index where the transformed Dmat will be stored. [jorb = R[isym](iorb)]
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jorb=srot(isym)%perm(iatom)-iatom+(imult+1)
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C Application of the symmetry operation :
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C ---------------------------------------
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C The transformation is : srot%rotrep.tmpmat(iorb).inverse(sort%rotrep) = Dmat(jorb)
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C or in other words, if R is a simple symmetry D(R[isym]) tmpmat(iorb) D(inverse(R[isym])) = Dmat(R[isym](iorb))
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C if R is multiplied by Theta D(R[isym]) tmpmat(iorb)* D(inverse(R[isym]))* = Dmat(R[isym](iorb))
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tmp_mat(1:2*(2*l+1),1:2*(2*l+1))=
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= MATMUL(tmp_mat(1:2*(2*l+1),1:2*(2*l+1)),
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& TRANSPOSE(CONJG(srot(isym)%rotrep(l,isrt)
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% %mat(1:2*(2*l+1),1:2*(2*l+1)) )) )
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sym_dmat(1:2*(2*l+1),1:2*(2*l+1),1,jorb)=
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= sym_dmat(1:2*(2*l+1),1:2*(2*l+1),1,jorb)+
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+ MATMUL( srot(isym)%rotrep(l,isrt)
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% %mat(1:2*(2*l+1),1:2*(2*l+1)) ,
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& tmp_mat(1:2*(2*l+1),1:2*(2*l+1)))
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DEALLOCATE(tmp_mat)
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ENDDO ! End of the isym loop
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ENDDO ! End of the imult loop
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C Renormalization of the symmetrized density matrices :
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C -----------------------------------------------------
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IF (nsym.gt.0) THEN
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DO imult=0,nmult(isrt)-1
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Dmat(1,iorb+imult)%mat(1:2*(2*l+1),1:2*(2*l+1))=
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= sym_dmat(1:2*(2*l+1),1:2*(2*l+1),1,imult+1)/nsym
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ENDDO
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ENDIF
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DEALLOCATE(sym_dmat)
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C Incrementation of the iorb index (for the while loop)
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iorb=iorb+nmult(isrt)
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C
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C ----------------------------------------------------------------------------------------------
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C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only) :
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C ----------------------------------------------------------------------------------------------
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ELSE
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C The table sym_dmat will store the symmetrized value of the density matrices of Dmat
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C associated to a same atomic sort isrt.
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ALLOCATE(sym_dmat(-l:l,-l:l,nsp,1:nmult(isrt)))
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sym_dmat=0.d0
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C Its size is nmult(isrt) because symmetry operations can transform the representants
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C of a same atomic sort one into another.
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C
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C Loop on the representants of the atomic sort isrt
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DO imult=0,nmult(isrt)-1
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iatom=orbit(iorb+imult)%atom
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C Loop on the symmetry operations of the system
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asym=0
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DO isym=1,nsym
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DO is=1,nsp
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ALLOCATE(tmp_mat(-l:l,-l:l))
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C If the calculation uses spin-polarized input files, the application of the symmetry operation
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C depends on the field srot%timeinv.
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IF(ifSP.AND.srot(isym)%timeinv) THEN
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C In this case (spin-polarized computation), the symmetry operation is block-diagonal in spin-space but
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C the time reversal operatot is included.
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tmp_mat(-l:l,-l:l)=CONJG(
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& Dmat(is,iorb+imult)%mat(-l:l,-l:l))
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C because of antiunitarity of the operator, the conjugate of Dmat must be use
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ELSE
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tmp_mat(-l:l,-l:l)=
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& Dmat(is,iorb+imult)%mat(-l:l,-l:l)
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ENDIF
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C
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C Definition of the index where the transformed Dmat will be stored. [jorb = R[isym](iorb)]
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jorb=srot(isym)%perm(iatom)-iatom+(imult+1)
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C
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C Computation of the phase factors in the case of a SO computation :
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C ------------------------------------------------------------------
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C For up/up and dn/dn blocks, no phase factor is needed.
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ephase=1.d0
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C For the up/dn block, initialisation of the phase factor
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IF(is==3) THEN
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ephase=EXP(CMPLX(0d0,srot(isym)%phase))
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C if srot%timeinv = .TRUE. , phase= g-a = 2pi+(alpha-gamma) and ephase = exp(+i(g-a)) = exp(+i(alpha-gamma))
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C if srot%timeinv = .FALSE., phase= a+g = 2pi-(alpha+gamma) and ephase = exp(+i(a+g)) = exp(-i(alpha+gamma))
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ENDIF
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C For the dn/up block, initialisation of the phase factor
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IF(is==4) THEN
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ephase=EXP(CMPLX(0d0,-srot(isym)%phase))
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C if srot%timeinv = .TRUE. , phase= g-a = 2pi+(alpha-gamma) and ephase = exp(-i(g-a)) = exp(-i(alpha-gamma))
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C if srot%timeinv = .FALSE., phase= a+g = 2pi-(alpha+gamma) and ephase = exp(-i(a+g)) = exp(+i(alpha+gamma))
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ENDIF
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C
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C Application of the symmetry operation which changes iorb in jorb :
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C ------------------------------------------------------------------
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C The transformation is : srot%rotrep.tmpmat(iorb).inverse(sort%rotrep) = Dmat(jorb)
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C or in other words, if R is a simple symmetry D(R[isym]) tmpmat(iorb) D(inverse(R[isym])) = Dmat(R[isym](iorb))
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C if R is multiplied by T D(R[isym]) tmpmat(iorb)* D(inverse(R[isym]))* = Dmat(R[isym](iorb))
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tmp_mat(-l:l,-l:l)=
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= MATMUL(tmp_mat(-l:l,-l:l),
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& TRANSPOSE(CONJG( srot(isym)
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& %rotrep(l,isrt)%mat(-l:l,-l:l) )) )
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sym_dmat(-l:l,-l:l,is,jorb)=
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= sym_dmat(-l:l,-l:l,is,jorb)+
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+ MATMUL(srot(isym)%rotrep(l,isrt)%mat(-l:l,-l:l),
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& tmp_mat(-l:l,-l:l) )*ephase
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DEALLOCATE(tmp_mat)
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ENDDO ! End of the is loop
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ENDDO ! End of the isym loop
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ENDDO ! End of the imult loop
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C
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C Renormalization of the symmetrized density matrices :
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C -----------------------------------------------------
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IF (nsym.gt.0) THEN
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DO imult=0,nmult(isrt)-1
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DO is=1,nsp
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Dmat(is,iorb+imult)%mat(-l:l,-l:l)=
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= sym_dmat(-l:l,-l:l,is,imult+1)/(nsym-asym)
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ENDDO
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ENDDO
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ENDIF
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DEALLOCATE(sym_dmat)
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C Incrementation of the iorb index (for the while loop)
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iorb=iorb+nmult(isrt)
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ENDIF ! End of the type basis if-then-else
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C
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ENDDO ! End of the while(iorb) loop
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C
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C
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C =============================================================
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C Application of the time reversal operation if paramagnetism :
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C =============================================================
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C If the system is paramagnetic, the magnetic group of the system
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C is a type II Shubnikov group and time-reveral symmetry must be added
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C to achieve the complete symmetrization.
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IF (.not.ifSP) THEN
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CALL add_timeinv(Dmat,orbit,norbit)
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END IF
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C
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RETURN
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END
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