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dft_tools/fortran/dmftproj/timeinv.f
Olivier Parcollet 0e585ad9b4 First import. triqs 1.0 alpha1
2013-07-23 20:55:29 +02:00

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Fortran
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c ******************************************************************************
c
c TRIQS: a Toolbox for Research in Interacting Quantum Systems
c
c Copyright (C) 2011 by L. Pourovskii, V. Vildosola, C. Martins, M. Aichhorn
c
c TRIQS is free software: you can redistribute it and/or modify it under the
c terms of the GNU General Public License as published by the Free Software
c Foundation, either version 3 of the License, or (at your option) any later
c version.
c
c TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
c WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
c FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
c details.
c
c You should have received a copy of the GNU General Public License along with
c TRIQS. If not, see <http://www.gnu.org/licenses/>.
c
c *****************************************************************************/
SUBROUTINE timeinv_op(mat,lm,l,isrt)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine applies the time reversal operation to the %%
C %% matrix mat which is associated to the l orbital of the atomic %%
C %% isrt. (matrix size = lm) The matrix mat is assumed to already %%
C %% be in the desired basis associated to isrt. %%
C %% The calculation done is : %%
C %% reptrans*T*conjg((inv(reptrans))*conjg(mat) %%
C %% %%
C %% If isrt=0, the matrix mat is assumed to be in the spherical %%
C %% harmonics basis and no spin is considered. (lm = 2*l+1) %%
C %% The calculation done is then : T*conjg(mat) %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
USE common_data
USE reps
IMPLICIT NONE
INTEGER :: lm,l,isrt
COMPLEX(KIND=8), DIMENSION(1:lm,1:lm) :: mat
COMPLEX(KIND=8), DIMENSION(:,:), ALLOCATABLE :: tinv
COMPLEX(KIND=8), DIMENSION(:,:), ALLOCATABLE :: tmp_tinv
COMPLEX(KIND=8), DIMENSION(-l:l,-l:l) :: tmat
INTEGER :: m,n
C
C Definition of the complex conjugation operator in the spherical harmonic basis :
C --------------------------------------------------------------------------------
C
tmat = CMPLX(0.d0,0.d0)
DO m=-l,l
tmat(m,-m)=(-1)**m
END DO
C
C
C Calculation of the Time-reversal operator in the desired representation basis :
C -------------------------------------------------------------------------------
C
IF (isrt==0) THEN
C The case isrt=0 is a "default case" :
C mat is in the spherical harmonic basis (without spinor representation)
ALLOCATE(tinv(1:2*l+1,1:2*l+1))
tinv(1:2*l+1,1:2*l+1)=tmat(-l:l,-l:l)
ELSE
C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) )
IF (reptrans(l,isrt)%ifmixing) THEN
ALLOCATE(tinv(1:2*(2*l+1),1:2*(2*l+1)))
ALLOCATE(tmp_tinv(1:2*(2*l+1),1:2*(2*l+1)))
tinv = CMPLX(0.d0,0.d0)
tmp_tinv = CMPLX(0.d0,0.d0)
C Definition of the time-reversal operator as a spinor-operator (multiplication by -i.sigma_y)
tinv(1:2*l+1,2*l+2:2*(2*l+1))=-tmat(-l:l,-l:l)
tinv(2*l+2:2*(2*l+1),1:2*l+1)=tmat(-l:l,-l:l)
C The time reversal operator is put in the desired basis.
tmp_tinv(1:2*(2*l+1),1:2*(2*l+1))=MATMUL(
& reptrans(l,isrt)%transmat(1:2*(2*l+1),1:2*(2*l+1)),
& tinv(1:2*(2*l+1),1:2*(2*l+1)))
tinv(1:2*(2*l+1),1:2*(2*l+1))=MATMUL(
& tmp_tinv(1:2*(2*l+1),1:2*(2*l+1)),
& TRANSPOSE(reptrans(l,isrt)%transmat
& (1:2*(2*l+1),1:2*(2*l+1)) ) )
C the result tinv = (reptrans)*tinv*transpose(reptrans)
C or tinv_{new_i} = <new_i|lm> tinv_{lm} (<lm|new_i>)*
C which is exactly the expression of the spinor operator in the new basis.
DEALLOCATE(tmp_tinv)
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only)
ELSE
ALLOCATE(tinv(1:2*l+1,1:2*l+1))
ALLOCATE(tmp_tinv(-l:l,-l:l))
tinv = CMPLX(0.d0,0.d0)
tmp_tinv = CMPLX(0.d0,0.d0)
C The time reversal operator is put in the desired basis.
tmp_tinv(-l:l,-l:l)=MATMUL(
& reptrans(l,isrt)%transmat(-l:l,-l:l),
& tmat(-l:l,-l:l) )
tinv(1:2*l+1,1:2*l+1)=MATMUL(
& tmp_tinv(-l:l,-l:l),TRANSPOSE(
& reptrans(l,isrt)%transmat(-l:l,-l:l)) )
DEALLOCATE(tmp_tinv)
END IF
C the result tinv = (reptrans)*tinv*transpose(reptrans)
C or tinv_{new_i} = <new_i|lm> tinv_{lm} (<lm|new_i>)*
C which is exactly the expression of the operator in the new basis.
END IF
C
C
C Multiplication of the matrix mat by the time reversal operator :
C ----------------------------------------------------------------
C
mat(1:lm,1:lm) = MATMUL(
& tinv(1:lm,1:lm),CONJG(mat(1:lm,1:lm)) )
DEALLOCATE(tinv)
C The multiplication is the product of tinv and (mat)*
C
RETURN
END
SUBROUTINE add_timeinv(Dmat,orbit,norbit)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine calculates for each density matrix in Dmat %%
C %% its image by the time-reversal operator and adds it to the %%
C %% former one to get a time-symmetrized result. %%
C %% %%
C %% This operation is done only if the computation is paramagnetic %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
USE common_data
USE projections
USE symm
USE reps
IMPLICIT NONE
INTEGER :: norbit
TYPE(matrix), DIMENSION(nsp,norbit) :: Dmat
COMPLEX(KIND=8),DIMENSION(:,:,:), ALLOCATABLE :: rot_dmat
COMPLEX(KIND=8),DIMENSION(:,:), ALLOCATABLE :: time_op
COMPLEX(KIND=8),DIMENSION(:,:,:), ALLOCATABLE :: tmp_mat
COMPLEX(KIND=8):: ephase
TYPE(orbital), DIMENSION(norbit) :: orbit
INTEGER :: isym, iorb, iatom, jorb, is, is1, l, i
INTEGER :: isrt, jatom, imult, m
C
C
DO iorb=1,norbit
l=orbit(iorb)%l
isrt=orbit(iorb)%sort
iatom=orbit(iorb)%atom
C -----------------------------------------------------------------------------------
C The s-orbitals are a particular case of a "non-mixing" basis and are treated here :
C -----------------------------------------------------------------------------------
IF(l==0) THEN
IF (nsp==1) THEN
Dmat(1,iorb)%mat(1,1) =
& ( Dmat(1,iorb)%mat(1,1)+
& CONJG(Dmat(1,iorb)%mat(1,1)) )/2.d0
ELSE
ALLOCATE(tmp_mat(1,1,nsp))
tmp_mat=0.d0
C Application of the time-reversal operation
C ------------------------------------------
DO is=1,nsp
is1=is+(-1)**(is+1)
C the time reversal operation transforms up/up -1- in dn/dn -2- and up/dn -3- in dn/up -4- (and vice versa)
tmp_mat(1,1,is)=CONJG(Dmat(is1,iorb)%mat(1,1) )
IF (is.gt.2) tmp_mat(1,1,is)=-tmp_mat(1,1,is)
C Off diagonal blocks are multiplied by (-1).
ENDDO
C Symmetrization of Dmat :
C ------------------------
DO is=1,nsp
Dmat(is,iorb)%mat(1,1) = (Dmat(is,iorb)%mat(1,1)+
& tmp_mat(1,1,is) )/2.d0
ENDDO
DEALLOCATE(tmp_mat)
ENDIF
C -----------------------------------------------------------------------------------------------------
C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) ) :
C -----------------------------------------------------------------------------------------------------
ELSEIF (reptrans(l,isrt)%ifmixing) THEN
C Calculation of the time-reversal operator :
C -------------------------------------------
ALLOCATE(time_op(1:2*(2*l+1),1:2*(2*l+1)))
time_op(:,:)=0.d0
DO m=1,2*(2*l+1)
time_op(m,m)=1.d0
ENDDO
C time_op is Identity.
CALL timeinv_op(time_op,2*(2*l+1),l,isrt)
C time_op is now the time-reversal operator in the desired basis ({new_i})
C
C Application of the time-reversal operation
C ------------------------------------------
ALLOCATE(tmp_mat(1:2*(2*l+1),1:2*(2*l+1),1))
tmp_mat(1:2*(2*l+1),1:2*(2*l+1),1)=
= MATMUL(Dmat(1,iorb)%mat(1:2*(2*l+1),1:2*(2*l+1)),
& TRANSPOSE(time_op(1:2*(2*l+1),1:2*(2*l+1)) ) )
tmp_mat(1:2*(2*l+1),1:2*(2*l+1),1)=
= MATMUL(time_op(1:2*(2*l+1),1:2*(2*l+1)),
& CONJG(tmp_mat(1:2*(2*l+1),1:2*(2*l+1),1) ) )
C The operation performed is : time_op.conjugate(Dmat).transpose(conjugate(time_op))
C or in other words, D(T)_{new_i} . Dmat* . D(inverse(T))*_{new_i}
C
C Symmetrization of Dmat :
C ------------------------
Dmat(1,iorb)%mat(1:2*(2*l+1),1:2*(2*l+1)) =
& ( Dmat(1,iorb)%mat(1:2*(2*l+1),1:2*(2*l+1)) +
& tmp_mat(1:2*(2*l+1),1:2*(2*l+1),1) )/2.d0
DEALLOCATE(tmp_mat)
DEALLOCATE(time_op)
C ----------------------------------------------------------------------------------------------
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only) :
C ----------------------------------------------------------------------------------------------
ELSE
C Calculation of the time-reversal operator :
C -------------------------------------------
ALLOCATE(time_op(-l:l,-l:l))
time_op(:,:)=0.d0
DO m=-l,l
time_op(m,m)=1.d0
ENDDO
C time_op is Identity.
CALL timeinv_op(time_op,(2*l+1),l,isrt)
C time_op is now the time-reversal operator in the desired basis ({new_i})
C
IF (nsp==1) THEN
C Application of the time-reversal operation and symmetrization :
C ---------------------------------------------------------------
ALLOCATE(tmp_mat(-l:l,-l:l,1))
tmp_mat(-l:l,-l:l,1)=
= MATMUL( Dmat(1,iorb)%mat(-l:l,-l:l),
& TRANSPOSE(time_op(-l:l,-l:l) ) )
tmp_mat(-l:l,-l:l,1)=
= MATMUL(time_op(-l:l,-l:l),
& CONJG(tmp_mat(-l:l,-l:l,1)) )
C The operation performed is : time_op.conjugate(Dmat).transpose(conjugate(time_op))
C or in other words, D(T)_{new_i} . Dmat* . D(inverse(T))*_{new_i}
Dmat(1,iorb)%mat(-l:l,-l:l) =
& ( Dmat(1,iorb)%mat(-l:l,-l:l) +
& tmp_mat(-l:l,-l:l,1) )/2.d0
DEALLOCATE(tmp_mat)
ELSE
C Application of the time-reversal operation
C ------------------------------------------
ALLOCATE(tmp_mat(-l:l,-l:l,nsp))
DO is=1,nsp
is1=is+(-1)**(is+1)
C the time reversal operation transforms up/up -1- in dn/dn -2- and up/dn -3- in dn/up -4 (and vice versa)
tmp_mat(-l:l,-l:l,is)=
= MATMUL( Dmat(is1,iorb)%mat(-l:l,-l:l),
& TRANSPOSE( time_op(-l:l,-l:l) ) )
tmp_mat(-l:l,-l:l,is)=
= MATMUL( time_op(-l:l,-l:l),
& CONJG( tmp_mat(-l:l,-l:l,is) ) )
C The operation performed is : time_op.conjugate(Dmat).transpose(conjugate(time_op))
C or in other words, D(T)_{new_i} . Dmat* . D(inverse(T))*_{new_i}
IF (is.gt.2) THEN
tmp_mat(-l:l,-l:l,is)=-tmp_mat(-l:l,-l:l,is)
ENDIF
C Off diagonal terms are multiplied by (-1).
ENDDO
C Symmetrization of Dmat :
C ------------------------
DO is=1,nsp
Dmat(is,iorb)%mat(-l:l,-l:l) =
& (Dmat(is,iorb)%mat(-l:l,-l:l)+
& tmp_mat(-l:l,-l:l,is) )/2.d0
ENDDO
DEALLOCATE(tmp_mat)
ENDIF
DEALLOCATE(time_op)
C
ENDIF ! End of the type basis if-then-else
ENDDO ! End of the iorb loop
C
RETURN
END
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