mirror of
https://github.com/triqs/dft_tools
synced 2024-08-31 00:03:43 +02:00
240 lines
11 KiB
FortranFixed
240 lines
11 KiB
FortranFixed
![]() |
|
||
|
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 rotdens_mat(Dmat,orbit,norbit)
|
||
|
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
C %% %%
|
||
|
C %% This subroutine applies to each density matrix in Dmat %%
|
||
|
C %% the transformation to go from the global coordinates to the %%
|
||
|
C %% local coordinates associated to the considered orbital. %%
|
||
|
C %% %%
|
||
|
C %% This version can be used for SO computations. %%
|
||
|
C %% %%
|
||
|
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
|
||
|
C Definition 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 :: tmp_mat
|
||
|
COMPLEX(KIND=8):: ephase
|
||
|
REAL(KIND=8):: factor
|
||
|
TYPE(orbital), DIMENSION(norbit) :: orbit
|
||
|
INTEGER :: iatom, isrt, iorb, is, is1, l, i, m
|
||
|
C
|
||
|
C
|
||
|
DO iorb=1,norbit
|
||
|
l=orbit(iorb)%l
|
||
|
isrt=orbit(iorb)%sort
|
||
|
iatom=orbit(iorb)%atom
|
||
|
C
|
||
|
IF(ifSP.AND.ifSO) THEN
|
||
|
C In this case, the complete spinor rotation approach (matrices of size 2*(2*l+1) ) is used for rotloc.
|
||
|
IF (l==0) THEN
|
||
|
C ------------------------------------------------------------------------------------------------------------
|
||
|
C For the s orbital, the spinor rotation matrix will be constructed directly from the Euler angles a,b and c :
|
||
|
C ------------------------------------------------------------------------------------------------------------
|
||
|
C Up/dn and Dn/up terms
|
||
|
ALLOCATE(tmp_mat(1:2,1:2))
|
||
|
ALLOCATE(rot_dmat(1:2,1:2))
|
||
|
IF (rotloc(iatom)%timeinv) THEN
|
||
|
factor=(rotloc(iatom)%a+rotloc(iatom)%g)/2.d0
|
||
|
tmp_mat(2,1)=EXP(CMPLX(0.d0,factor))*
|
||
|
& DCOS(rotloc(iatom)%b/2.d0)
|
||
|
tmp_mat(1,2)=-CONJG(tmp_mat(2,1))
|
||
|
C Up/dn and Dn/up terms
|
||
|
factor=-(rotloc(iatom)%a-rotloc(iatom)%g)/2.d0
|
||
|
tmp_mat(2,2)=-EXP(CMPLX(0.d0,factor))*
|
||
|
& DSIN(rotloc(iatom)%b/2.d0)
|
||
|
tmp_mat(1,1)=CONJG(tmp_mat(2,2))
|
||
|
C definition of the total density matrix
|
||
|
rot_dmat(1,1)=Dmat(1,iorb)%mat(1,1)
|
||
|
rot_dmat(2,2)=Dmat(2,iorb)%mat(1,1)
|
||
|
rot_dmat(1,2)=Dmat(3,iorb)%mat(1,1)
|
||
|
rot_dmat(2,1)=Dmat(4,iorb)%mat(1,1)
|
||
|
C going to the local basis
|
||
|
rot_dmat(1:2,1:2)=CONJG(MATMUl(
|
||
|
& rot_dmat(1:2,1:2),tmp_mat(1:2,1:2)))
|
||
|
rot_dmat(1:2,1:2)=MATMUl(
|
||
|
& TRANSPOSE(tmp_mat(1:2,1:2)),
|
||
|
& rot_dmat(1:2,1:2))
|
||
|
ELSE
|
||
|
factor=(rotloc(iatom)%a+rotloc(iatom)%g)/2.d0
|
||
|
tmp_mat(1,1)=EXP(CMPLX(0.d0,factor))*
|
||
|
& DCOS(rotloc(iatom)%b/2.d0)
|
||
|
tmp_mat(2,2)=CONJG(tmp_mat(1,1))
|
||
|
C Up/dn and Dn/up terms
|
||
|
factor=-(rotloc(iatom)%a-rotloc(iatom)%g)/2.d0
|
||
|
tmp_mat(1,2)=EXP(CMPLX(0.d0,factor))*
|
||
|
& DSIN(rotloc(iatom)%b/2.d0)
|
||
|
tmp_mat(2,1)=-CONJG(tmp_mat(1,2))
|
||
|
C definition of the total density matrix
|
||
|
rot_dmat(1,1)=Dmat(1,iorb)%mat(1,1)
|
||
|
rot_dmat(2,2)=Dmat(2,iorb)%mat(1,1)
|
||
|
rot_dmat(1,2)=Dmat(3,iorb)%mat(1,1)
|
||
|
rot_dmat(2,1)=Dmat(4,iorb)%mat(1,1)
|
||
|
C going to the local basis
|
||
|
rot_dmat(1:2,1:2)=MATMUl(
|
||
|
& TRANSPOSE(CONJG(tmp_mat(1:2,1:2))),
|
||
|
& rot_dmat(1:2,1:2))
|
||
|
rot_dmat(1:2,1:2)=MATMUl(
|
||
|
& rot_dmat(1:2,1:2),tmp_mat(1:2,1:2))
|
||
|
ENDIF
|
||
|
DEALLOCATE(tmp_mat)
|
||
|
C storing in Dmat
|
||
|
Dmat(1,iorb)%mat(1,1)=rot_dmat(1,1)
|
||
|
Dmat(2,iorb)%mat(1,1)=rot_dmat(2,2)
|
||
|
Dmat(3,iorb)%mat(1,1)=rot_dmat(1,2)
|
||
|
Dmat(4,iorb)%mat(1,1)=rot_dmat(2,1)
|
||
|
DEALLOCATE(rot_dmat)
|
||
|
ELSE
|
||
|
C -----------------------------------------------------------------------------------------------------
|
||
|
C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) ) :
|
||
|
C -----------------------------------------------------------------------------------------------------
|
||
|
IF (reptrans(l,isrt)%ifmixing) THEN
|
||
|
C We use the complete spin-space representation, so no trick on indices is necessary.
|
||
|
C
|
||
|
C Application of the operation inverse(Rloc).Dmat.(Rloc) :
|
||
|
C -------------------------------------------------------
|
||
|
IF (rotloc(iatom)%timeinv) THEN
|
||
|
C In this case, the operators is antiunitary [ inverse(R)=transpose(R) ]
|
||
|
Dmat(1,iorb)%mat(:,:)=CONJG(
|
||
|
= MATMUL(Dmat(1,iorb)%mat(:,:),
|
||
|
& rotloc(iatom)%rotrep(l)%mat(:,:) ))
|
||
|
Dmat(1,iorb)%mat(:,:)=
|
||
|
= MATMUL(TRANSPOSE( rotloc(iatom)%
|
||
|
& rotrep(l)%mat(:,:) ),Dmat(1,iorb)%mat(:,:) )
|
||
|
C Dmat_{local} = inverse(Rloc) Dmat_{global}* Rloc*
|
||
|
C Dmat_{local} = transpose(Rloc) Dmat_{global}* Rloc*
|
||
|
ELSE
|
||
|
C In this case, all the operators are unitary [ inverse(R)=transpose(conjugate(R)) ]
|
||
|
Dmat(1,iorb)%mat(:,:)=
|
||
|
= MATMUL(Dmat(1,iorb)%mat(:,:),
|
||
|
& rotloc(iatom)%rotrep(l)%mat(:,:) )
|
||
|
Dmat(1,iorb)%mat(:,:)=
|
||
|
= MATMUL(TRANSPOSE(CONJG( rotloc(iatom)%
|
||
|
& rotrep(l)%mat(:,:) )),Dmat(1,iorb)%mat(:,:) )
|
||
|
C Dmat_{local} = <x_local | x_global> Dmat_{global} <x_global | x_local>
|
||
|
C Dmat_{local} = inverse(Rloc) Dmat_{global} Rloc
|
||
|
ENDIF
|
||
|
C
|
||
|
ELSE
|
||
|
C ----------------------------------------------------------------------------------------------
|
||
|
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only) :
|
||
|
C ----------------------------------------------------------------------------------------------
|
||
|
C definition of the total density matrix
|
||
|
ALLOCATE(rot_dmat(1:2*(2*l+1),1:2*(2*l+1)))
|
||
|
rot_dmat(1:(2*l+1),1:(2*l+1))=
|
||
|
& Dmat(1,iorb)%mat(-l:l,-l:l)
|
||
|
rot_dmat(2*l+2:2*(2*l+1),2*l+2:2*(2*l+1))=
|
||
|
& Dmat(2,iorb)%mat(-l:l,-l:l)
|
||
|
rot_dmat(1:(2*l+1),2*l+2:2*(2*l+1))=
|
||
|
& Dmat(3,iorb)%mat(-l:l,-l:l)
|
||
|
rot_dmat(2*l+2:2*(2*l+1),1:(2*l+1))=
|
||
|
& Dmat(4,iorb)%mat(-l:l,-l:l)
|
||
|
IF (rotloc(iatom)%timeinv) THEN
|
||
|
C In this case, the operator is antiunitary [ inverse(R)=transpose(R) ]
|
||
|
rot_dmat(1:2*(2*l+1),1:2*(2*l+1))=CONJG(
|
||
|
= MATMUL(rot_dmat(1:2*(2*l+1),1:2*(2*l+1)),
|
||
|
& rotloc(iatom)%rotrep(l)
|
||
|
& %mat(1:2*(2*l+1),1:2*(2*l+1)) ))
|
||
|
rot_dmat(1:2*(2*l+1),1:2*(2*l+1))=
|
||
|
= MATMUL(TRANSPOSE( rotloc(iatom)%
|
||
|
& rotrep(l)%mat(1:2*(2*l+1),1:2*(2*l+1)) ),
|
||
|
& rot_dmat(1:2*(2*l+1),1:2*(2*l+1)) )
|
||
|
C Dmat_{local} = inverse(Rloc) Dmat_{global}* Rloc*
|
||
|
C Dmat_{local} = transpose(Rloc) Dmat_{global}* Rloc*
|
||
|
ELSE
|
||
|
C In this case, all the operators are unitary [ inverse(R)=transpose(conjugate(R)) ]
|
||
|
rot_dmat(1:2*(2*l+1),1:2*(2*l+1))=
|
||
|
= MATMUL(rot_dmat(1:2*(2*l+1),1:2*(2*l+1)),
|
||
|
& rotloc(iatom)%rotrep(l)
|
||
|
& %mat(1:2*(2*l+1),1:2*(2*l+1)) )
|
||
|
rot_dmat(1:2*(2*l+1),1:2*(2*l+1))=
|
||
|
= MATMUL(TRANSPOSE(CONJG( rotloc(iatom)%
|
||
|
& rotrep(l)%mat(1:2*(2*l+1),1:2*(2*l+1)) )),
|
||
|
& rot_dmat(1:2*(2*l+1),1:2*(2*l+1)) )
|
||
|
C Dmat_{local} = <x_local | x_global> Dmat_{global} <x_global | x_local>
|
||
|
C Dmat_{local} = inverse(Rloc) Dmat_{global} Rloc
|
||
|
ENDIF
|
||
|
C storing in dmat again
|
||
|
Dmat(1,iorb)%mat(-l:l,-l:l)=
|
||
|
& rot_dmat(1:(2*l+1),1:(2*l+1))
|
||
|
Dmat(2,iorb)%mat(-l:l,-l:l)=
|
||
|
& rot_dmat(2*l+2:2*(2*l+1),2*l+2:2*(2*l+1))
|
||
|
Dmat(3,iorb)%mat(-l:l,-l:l)=
|
||
|
& rot_dmat(1:(2*l+1),2*l+2:2*(2*l+1))
|
||
|
Dmat(4,iorb)%mat(-l:l,-l:l)=
|
||
|
& rot_dmat(2*l+2:2*(2*l+1),1:(2*l+1))
|
||
|
DEALLOCATE(rot_dmat)
|
||
|
ENDIF ! End of the if mixing if-then-else
|
||
|
ENDIF ! End of the if "l=0" if-then-else
|
||
|
ELSE
|
||
|
C ------------------------------------------------------------------------------
|
||
|
C The s-orbitals are a particular case of a "non-mixing" basis and is invariant.
|
||
|
C ------------------------------------------------------------------------------
|
||
|
IF(l==0) CYCLE
|
||
|
C ----------------------------------------------------------------------------------------------
|
||
|
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only) :
|
||
|
C ----------------------------------------------------------------------------------------------
|
||
|
ALLOCATE(rot_dmat(-l:l,-l:l))
|
||
|
DO is=1,nsp
|
||
|
rot_dmat=0.d0
|
||
|
C
|
||
|
C Application of the operation inverse(Rloc).Dmat.(Rloc) :
|
||
|
C -------------------------------------------------------
|
||
|
C In this case, (either a paramagnetic calculation or a spin-polarized one
|
||
|
C but the symmetry operation does not change the magntization direction)
|
||
|
C all the operators are unitary [ inverse(R)=transpose(conjugate(R)) ]
|
||
|
rot_dmat(-l:l,-l:l)=
|
||
|
= MATMUL(Dmat(is,iorb)%mat(-l:l,-l:l),
|
||
|
& rotloc(iatom)%rotrep(l)%mat(-l:l,-l:l) )
|
||
|
rot_dmat(-l:l,-l:l)=
|
||
|
= MATMUL(TRANSPOSE(CONJG( rotloc(iatom)%
|
||
|
& rotrep(l)%mat(-l:l,-l:l) )),
|
||
|
& rot_dmat(-l:l,-l:l) )
|
||
|
C rotmat_{local} = <x_local | x_global> rotmat_{global} <x_global | x_local>
|
||
|
C rotmat_{local} = inverse(Rloc) rotmat_{global} Rloc
|
||
|
C
|
||
|
C Storing the new value in Dmat :
|
||
|
C -------------------------------
|
||
|
Dmat(is,iorb)%mat(-l:l,-l:l)=rot_dmat(-l:l,-l:l)
|
||
|
ENDDO
|
||
|
DEALLOCATE(rot_dmat)
|
||
|
C
|
||
|
ENDIF ! End of the ifSO-ifSP if-then-else
|
||
|
ENDDO ! End of the iorb loop
|
||
|
C
|
||
|
RETURN
|
||
|
END
|
||
|
|
||
|
|
||
|
|
||
|
|
||
|
|