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