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 .
c
c *****************************************************************************/
SUBROUTINE set_ang_trans
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine sets up the matrices for transformation between %%
C %% the default complex spherical harmonics used in Wien2k and an %%
C %% angular basis chosen, for each orbital of each atom. %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
USE common_data
USE file_names
USE reps
USE prnt
IMPLICIT NONE
CHARACTER(len=150) :: fullpath
CHARACTER(len=250) :: buf1
CHARACTER(len=25) :: basis_file
CHARACTER(len=1) :: repsign
INTEGER, DIMENSION(2*(2*lmax+1)) :: degrep
REAL(KIND=8), DIMENSION(:), ALLOCATABLE :: rtrans,itrans
INTEGER :: m, l, m1, irep, isrt, ind, ind1, ind2
COMPLEX(KIND=8),DIMENSION(:,:), ALLOCATABLE :: tempmat
LOGICAL :: flag
C
C
WRITE(buf,'(a)')'======================================='
CALL printout(0)
WRITE(buf,'(a)')'Basis representation for each sort.'
CALL printout(0)
CALL printout(0)
C =================================
C Creation of the reptrans matrix :
C =================================
C
C For the s-electrons : no transformation is necessary (it's always the scalar 1)
ALLOCATE(reptrans(1:lmax,1:nsort))
C Definition of the size of reptrans (size lmax*nsort)
C Each element of this table is an "ang_bas" element, which will be defined below.
DO isrt=1,nsort
C -----------------------------------------------
C Case of a representation in the complex basis :
C -----------------------------------------------
IF (defbasis(isrt)%typebasis(1:7)=='complex') THEN
DO l=1,lmax
IF (lsort(l,isrt)==0) THEN
C The considered orbital is not included, all the fields are set up to default value.
reptrans(l,isrt)%nreps=1
ALLOCATE(reptrans(l,isrt)%dreps(1))
ALLOCATE(reptrans(l,isrt)%transmat(1,1))
reptrans(l,isrt)%transmat=0d0
reptrans(l,isrt)%dreps(1)=0
reptrans(l,isrt)%ifmixing=.FALSE.
ELSE
C The considered orbital is included.
reptrans(l,isrt)%nreps=1
ALLOCATE(reptrans(l,isrt)%dreps(1))
ALLOCATE(reptrans(l,isrt)%transmat(-l:l,-l:l))
reptrans(l,isrt)%transmat=0d0
reptrans(l,isrt)%dreps(1)=2*l+1
reptrans(l,isrt)%ifmixing=.FALSE.
DO m=-l,l
reptrans(l,isrt)%transmat(m,m)=1d0
ENDDO
C In this case, the transformation matrix is just the Identity (hence 1 irep).
C Spin up and Spin down states are not mixed in the basis representation.
ENDIF
ENDDO
C ---------------------------------------------
C Case of a representation in the cubic basis :
C ---------------------------------------------
ELSEIF (defbasis(isrt)%typebasis(1:5)=='cubic') THEN
DO l=1,lmax
IF (lsort(l,isrt)==0) THEN
C The considered orbital is not included, all the fields are set up to default value.
reptrans(l,isrt)%nreps=1
ALLOCATE(reptrans(l,isrt)%dreps(1))
ALLOCATE(reptrans(l,isrt)%transmat(1,1))
reptrans(l,isrt)%transmat=0d0
reptrans(l,isrt)%dreps(1)=0
reptrans(l,isrt)%ifmixing=.FALSE.
ELSE
C The considered orbital is included.
C The cubic basis is described in the format transpose(P) where P is the usual matrix
C of the eigenvectors of a matrix D ( D.P=Delta.P with Delta diagonal or P=).
C In other words, each line of the file describes the coefficient of the "new basis vector"
C in the basis { |l,-l,up>,...|l,l,up>,|l,-l,dn>,...|l,l,dn> }.
C The transformation matrices are stored in the directory SRC_templates, the variable "fullpath"
C must be updated if this prgm is copied.
ALLOCATE(reptrans(l,isrt)%transmat(-l:l,-l:l))
ALLOCATE(rtrans(-l:l))
ALLOCATE(itrans(-l:l))
C write(*,*)fullpath
IF (l==1) CALL
& set_harm_file(fullpath,'case.cf_p_cubic')
C standard cubic representation of p electrons : px,py,pz
IF (l==2) CALL
& set_harm_file(fullpath,'case.cf_d_eg_t2g')
C standard cubic representation of d-electrons : dz2, dx2-y2, dxy, dxz,dyz (Wien-convention for the phase)
IF (l==3) CALL
& set_harm_file(fullpath,'case.cf_f_mm2')
C mm2 representation of the f electrons (standard definition with complex coefficients)
C
C Reading of the file
OPEN(iumatfile,file=fullpath,status='old')
ind=-l
irep=0
m = -l
DO WHILE (m.le.l)
READ(iumatfile,'(a)')buf1
READ(buf1(1:1),'(a)')repsign
C Get rid of comment lines first
IF (repsign.NE.'#') THEN
IF(repsign=='*') THEN
C Finding the different ireps in the new basis (a "*" means the end of an irep)
irep=irep+1
degrep(irep)=m-ind+1
ind=m+1
ENDIF
READ(buf1(2:250),*)(rtrans(m1),itrans(m1),m1=-l,l)
C The line of the file is stored in the column of reptrans, which is temporarly "P".
reptrans(l,isrt)%transmat(-l:l,m)=
& CMPLX(rtrans(-l:l),itrans(-l:l))
m = m + 1
ENDIF
ENDDO
reptrans(l,isrt)%transmat(-l:l,-l:l)=
= TRANSPOSE(CONJG(reptrans(l,isrt)%transmat(-l:l,-l:l)))
C reptrans%transmat = inverse(P) = , the transformation matrix from complex basis to the cubic one.
C ( inverse(P) is the decomposition of the complex basis in the new basis...)
reptrans(l,isrt)%nreps=irep
ALLOCATE(reptrans(l,isrt)%dreps(irep))
reptrans(l,isrt)%dreps(1:irep)=degrep(1:irep)
reptrans(l,isrt)%ifmixing=.FALSE.
C reptrans%nreps = the total number of ireps in the cubic basis
C reptrans%dreps = table of the size of the different ireps
C reptrans%ifmixing = .FALSE. because Spin up and Spin down states are not mixed in the basis representation.
CLOSE(iumatfile)
DEALLOCATE(rtrans)
DEALLOCATE(itrans)
ENDIF
ENDDO
C ---------------------------------------------------------
C Case of a representation defined in an added input file :
C ---------------------------------------------------------
ELSEIF (defbasis(isrt)%typebasis(1:8)=='fromfile') THEN
basis_file=defbasis(isrt)%sourcefile
OPEN(iumatfile,file=basis_file,status='old')
DO l=1,lmax
IF (lsort(l,isrt)==0) THEN
C The considered orbital is not included, all the fields are set up to default value.
reptrans(l,isrt)%nreps=1
ALLOCATE(reptrans(l,isrt)%dreps(1))
ALLOCATE(reptrans(l,isrt)%transmat(1,1))
reptrans(l,isrt)%transmat=0d0
reptrans(l,isrt)%dreps(1)=0
ELSE
C The considered orbital is included.
C The new basis is described in the format transpose(P) where P is the usual matrix
C of the eigenvectors of a matrix D ( D.P=Delta.P with Delta diagonal or P=).
C In other words, each line of the file describes the coefficient of the "new basis vector"
C in the basis { |l,-l,up>,...|l,l,up>,|l,-l,dn>,...|l,l,dn> }.
C The transformation matrices are stored in the directory SRC_templates, the variable "fullpath"
C must be updated if this prgm is copied.
ind=1
irep=0
ALLOCATE(tempmat(1:2*(2*l+1),1:2*(2*l+1)))
ALLOCATE(rtrans(1:2*(2*l+1)))
ALLOCATE(itrans(1:2*(2*l+1)))
C
C Reading of the file
DO m=1,2*(2*l+1)
READ(iumatfile,'(a)')buf1
READ(buf1(1:1),'(a)')repsign
IF(repsign=='*') THEN
C Finding the different ireps in the new basis (a "*" means the end of an irep)
irep=irep+1
degrep(irep)=m-ind+1
ind=m+1
ENDIF
READ(buf1(2:250),*)(rtrans(m1),itrans(m1),
& m1=1,2*(2*l+1))
tempmat(1:2*(2*l+1),m)=
= CMPLX(rtrans(1:2*(2*l+1)),itrans(1:2*(2*l+1)))
C The lines of the read matrix are stored in the column of tempmat, which is then P.
ENDDO
C
C Determination if the basis mixes Spin up and Spin down states
flag=.TRUE.
ind1=1
ind2=1
C The "do while" loop stops when flag=FALSE or i=2*(l+1)
DO WHILE (flag.AND.(ind1.lt.2*(l+1)))
flag=flag.AND.
& (tempmat((2*l+1)+ind1,(2*l+1)+ind2)==tempmat(ind1,ind2))
flag=flag.AND.(tempmat((2*l+1)+ind1,ind2)==0.d0)
flag=flag.AND.(tempmat(ind1,(2*l+1)+ind2)==0.d0)
IF (ind2==(2*l+1)) THEN
ind1=ind1+1
ind2=1
ELSE
ind2=ind2+1
END IF
ENDDO
IF (flag) THEN
C If flag=TRUE (then i=2*l+2), the tempmat matrix is block diagonal in spin with
C the condition block up/up = block down/down.
C The Spin up and Spin down states are not mixed in the basis representation.
reptrans(l,isrt)%ifmixing=.FALSE.
C reptrans%ifmixing = .FALSE. because Spin up and Spin down states are not mixed in the basis representation.
C
C ---------------------------------------------------------------------------------------
C Interruption of the prgm if the basis description is not correct.
C -------------------------
C
IF (SUM(degrep(1:irep/2)).ne.(2*l+1)) THEN
WRITE(buf,'(a,a,i2,a,i2,a)')'The basis description ',
& 'for isrt = ',isrt,' and l = ',l,' is not recognized.'
CALL printout(0)
WRITE(buf,'(a,a)')'Check the structure of the file ',
& defbasis(isrt)%sourcefile
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
END IF
C ---------------------------------------------------------------------------------------
C
ALLOCATE(reptrans(l,isrt)%transmat(-l:l,-l:l))
reptrans(l,isrt)%transmat(-l:l,-l:l)=
= tempmat(1:(2*l+1),1:(2*l+1))
reptrans(l,isrt)%transmat(-l:l,-l:l)=
= TRANSPOSE(CONJG(reptrans(l,isrt)%transmat(-l:l,-l:l)))
C The up/up block is enough to describe the transformation (as for cubic or complex bases)
C reptrans%transmat = inverse(P) =
C inverse(P) is indeed the decomposition of the complex basis in the new basis.
reptrans(l,isrt)%nreps=irep/2
ALLOCATE(reptrans(l,isrt)%dreps(reptrans(l,isrt)%nreps))
reptrans(l,isrt)%dreps(1:reptrans(l,isrt)%nreps)=
= degrep(1:reptrans(l,isrt)%nreps)
C reptrans%nreps = the number of ireps in the desired basis for up spin
C reptrans%dreps = table of the size of the different ireps for up spin
ELSE
C If flag=FALSE, either the tempmat matrix either mixes Spin up and Spin down states
C or the representation basis for Spin up and Spin down states differ.
C In this case, it is not possible to reduce the description only to the up/up block.
C The whole tempmat matrix is necessary.
C
C ---------------------------------------------------------------------------------------
C Interruption of the prgm if the basis description is not correct.
C -------------------------
C
IF (SUM(degrep(1:irep)).ne.(2*(2*l+1))) THEN
WRITE(buf,'(a,a,i2,a,i2,a)')'The basis description ',
& 'for isrt = ',isrt,' and l = ',l,' is not recognized.'
CALL printout(0)
WRITE(buf,'(a,a)')'Check the structure of the file ',
& defbasis(isrt)%sourcefile
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
END IF
C ---------------------------------------------------------------------------------------
C
reptrans(l,isrt)%ifmixing=.TRUE.
C reptrans%ifmixing = .TRUE. because Spin up and Spin down states are mixed in the basis representation.
ALLOCATE(reptrans(l,isrt)%transmat
& (1:2*(2*l+1),1:2*(2*l+1)))
reptrans(l,isrt)%transmat(1:2*(2*l+1),1:2*(2*l+1))=
= tempmat(1:2*(2*l+1),1:2*(2*l+1))
reptrans(l,isrt)%transmat(1:2*(2*l+1),1:2*(2*l+1))=
= TRANSPOSE(CONJG(reptrans(l,isrt)%transmat
& (1:2*(2*l+1),1:2*(2*l+1))))
C In this case, reptrans%transmat is a square matrix which ranges from 1 to 2*(2*l+1).
C reptrans%transmat = inverse(P) =
C inverse(P) is indeed the decomposition of the complex basis in the new basis.
reptrans(l,isrt)%nreps=irep
ALLOCATE(reptrans(l,isrt)%dreps(irep))
reptrans(l,isrt)%dreps(1:irep)=degrep(1:irep)
C reptrans%nreps = the total number of ireps in the desired basis
C reptrans%dreps = table of the size of the different ireps
C
C Restriction for simplicity in the following (and for physical reasons) :
C a basis with ifmixing=.TRUE. is allowed only if the computation includes SO.
IF (.not.ifSO) THEN
WRITE(buf,'(a,a,i2,a,i2,a)')'The basis description ',
& 'for isrt = ',isrt,' and l = ',l,
& ' mixes up and down states.'
CALL printout(0)
WRITE(buf,'(a,a)')'This option can not ',
& 'be used in a computation without Spin-Orbit.'
CALL printout(0)
WRITE(buf,'(a,a)')'Modify the structure of the file ',
& defbasis(isrt)%sourcefile
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
END IF
END IF
DEALLOCATE(tempmat)
DEALLOCATE(rtrans)
DEALLOCATE(itrans)
ENDIF
ENDDO
CLOSE(iumatfile)
C ----------------------------------------------
C Case of a wrong definition in the input file :
C ----------------------------------------------
ELSE
C
C ---------------------------------------------------------------------------------------
C Interruption of the prgm if the file has not the expected structure.
C -------------------------
C
WRITE(buf,'(a,i2,a)')'The basis description for isrt = ',
& isrt,' is not recognized.'
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
ENDIF
C ---------------------------------------------------------------------------------------
C
ENDDO
C
C
C ===============================================
C Printing the basis representation information :
C ===============================================
C
DO isrt=1,nsort
IF (notinclude(isrt)) cycle
CALL printout(0)
WRITE(buf,'(a)')'-------------------------------------'
CALL printout(0)
WRITE(buf,'(a,i2,a)')'For the sort ',isrt,' :'
CALL printout(0)
IF (defbasis(isrt)%typebasis(1:7)=='complex') THEN
C -----------------------------------------------
C Case of a representation in the complex basis :
C -----------------------------------------------
WRITE(buf,'(a,i2,a)')'The atomic sort', isrt,
& ' is studied in the complex basis representation.'
CALL printout(0)
CALL printout(0)
ELSEIF (defbasis(isrt)%typebasis(1:5)=='cubic') THEN
C ---------------------------------------------
C Case of a representation in the cubic basis :
C ---------------------------------------------
WRITE(buf,'(a,i2,a)')'The atomic sort', isrt,
& ' is studied in the cubic basis representation.'
CALL printout(0)
CALL printout(0)
DO l=0,lmax
C The considered orbital is not included.
IF (lsort(l,isrt)==0) cycle
C Case of the s-electrons
IF (l==0) THEN
WRITE(buf,'(a,a,(F12.6))')'The basis for s-orbital ',
& 'is still',1.d0
CALL printout(0)
ELSE
C Case of the other orbitals
WRITE(buf,'(a,i2,a,a,a)')'The basis for orbital l=',l,
& ' has the following properties :'
CALL printout(0)
WRITE(buf,'(a,i2)')' - number of ireps : ',
& reptrans(l,isrt)%nreps
CALL printout(0)
WRITE(buf,'(a,14(i2,x))')' - degree of each ireps : ',
& reptrans(l,isrt)%dreps(1:reptrans(l,isrt)%nreps)
CALL printout(0)
WRITE(buf,'(a,a,a)')'The transformation matrix is block',
& ' diagonal in the spin-space. The up/up and down/down',
& ' blocks are the same and defined as :'
CALL printout(0)
C The transformation matrix "P = " is displayed.
DO m=-l,l
WRITE(buf,'(7(2F12.6),x)')
& CONJG(reptrans(l,isrt)%transmat(-l:l,m))
CALL printout(0)
ENDDO
CALL printout(0)
ENDIF
ENDDO
CALL printout(0)
ELSE
C ---------------------------------------------------------
C Case of a representation defined in an added input file :
C ---------------------------------------------------------
WRITE(buf,'(a,i2,a,a,a)')'The atomic sort', isrt,
& ' is studied in the basis representation',
& ' defined in the file ',
& defbasis(isrt)%sourcefile
CALL printout(0)
CALL printout(0)
DO l=0,lmax
C The considered orbital is not included.
IF (lsort(l,isrt)==0) cycle
C Case of the s-electrons
IF (l==0) THEN
WRITE(buf,'(a,a,(F12.6))')'The basis for s-orbital ',
& 'is still',1.d0
CALL printout(0)
CALL printout(0)
ELSE
C Case of the other orbitals
WRITE(buf,'(a,i2,a)')'The basis for orbital l=',l,
& ' has the following properties :'
CALL printout(0)
WRITE(buf,'(a,i2)')' - number of ireps : ',
& reptrans(l,isrt)%nreps
CALL printout(0)
WRITE(buf,'(a,14(i2,x))')' - degree of each ireps : ',
& reptrans(l,isrt)%dreps(1:reptrans(l,isrt)%nreps)
CALL printout(0)
IF (reptrans(l,isrt)%ifmixing) THEN
C If the whole matrix description is necessary.
WRITE(buf,'(a,a)')'The transformation matrix mixes',
& ' up and down states in the spin-space'
CALL printout(0)
WRITE(buf,'(a,a)') ' and is defined as : ',
& '[ block 1 | block 2 ] with'
CALL printout(0)
WRITE(buf,'(a,a)') ' ',
& '[ block 3 | block 4 ]'
CALL printout(0)
C The transformation matrix "P = " is displayed.
WRITE(buf,'(a,i2,a)') 'For the block 1 :'
CALL printout(0)
DO m=1,2*l+1
WRITE(buf,'(7(2F12.6),x)')
& CONJG(reptrans(l,isrt)%transmat(1:(2*l+1),m))
CALL printout(0)
ENDDO
WRITE(buf,'(a,i2,a)') 'For the block 2 :'
CALL printout(0)
DO m=1,2*l+1
WRITE(buf,'(7(2F12.6),x)')
& CONJG(reptrans(l,isrt)%transmat(2*l+2:2*(2*l+1),m))
CALL printout(0)
ENDDO
WRITE(buf,'(a,i2,a)') 'For the block 3 :'
CALL printout(0)
DO m=2*l+2,2*(2*l+1)
WRITE(buf,'(7(2F12.6),x)')
& CONJG(reptrans(l,isrt)%transmat(1:(2*l+1),m))
CALL printout(0)
ENDDO
WRITE(buf,'(a,i2,a)') 'For the block 4 :'
CALL printout(0)
DO m=2*l+2,2*(2*l+1)
WRITE(buf,'(7(2F12.6),x)')
& CONJG(reptrans(l,isrt)%
& transmat(2*l+2:2*(2*l+1),m))
CALL printout(0)
ENDDO
ELSE
C If the matrix description can be reduced to its up/up block.
WRITE(buf,'(a,a,a)')'The transformation matrix is block',
& ' diagonal in the spin-space. The up/up and down/down',
& ' blocks are the same and defined as :'
CALL printout(0)
C The transformation matrix "P = " is displayed.
DO m=-l,l
WRITE(buf,'(7(2F12.6),x)')
& CONJG(reptrans(l,isrt)%transmat(-l:l,m))
CALL printout(0)
ENDDO
ENDIF ! End of the ifmixing if-then-else
CALL printout(0)
ENDIF ! End of the l if-then-else
ENDDO ! End of the l loop
CALL printout(0)
ENDIF ! End of the basis description if-then-else
ENDDO ! End of the isrt loop
C
RETURN
END
SUBROUTINE set_harm_file(fullpath,filename)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine sets the fullpath variable %%
C %% Be careful, wien_path is defined in modules.f !!! %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
USE common_data, ONLY : wien_path
USE prnt
IMPLICIT NONE
CHARACTER(len=*) :: filename, fullpath
CHARACTER(len=*), PARAMETER :: dir='SRC_templates'
INTEGER :: i1, i2, i, i3
C
i1=LEN_TRIM(wien_path)
i2=LEN(dir)
i3=LEN(filename)
i=i1+i2+i3+2
IF(LEN(fullpath) < i) THEN
WRITE(buf,'(a)')
& 'Characters required for the basis transformation ',
& ' filename is too long.'
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
STOP
ENDIF
fullpath=' '
fullpath(1:i)=wien_path(1:i1)//'/'//dir//'/'//filename(1:i3)
END SUBROUTINE set_harm_file