./66_nonlocal/metric

ABINIT/metric_so

ABINIT/metric_so [ Functions ]

NAME

 metric_so

FUNCTION

 Computes Pauli matrices and antisymmetric tensor needed for
 spin-orbit.

 Copyright (C) 1998-2018 ABINIT group (DCA, XG, GZ, MT)
 This file is distributed under the terms of the
 GNU General Public License, see ~abinit/COPYING
 or http://www.gnu.org/copyleft/gpl.txt .
 For the initials of contributors, see ~abinit/doc/developers/contributors.txt.

INPUTS

  gprimd(3,3)=dimensional primitive translations for reciprocal space
              (bohr**-1)

OUTPUT

  amet(2,3,3,2,2)=the antisymmetric tensor A(Re/Im,y,y'',s,s'')
  pauli(2,2,2,3)=Pauli matrixes

NOTES

 (the preprocessing based on CPP does not allow isolated quotes,
  so that they have been doubled in the following latex equations)
 $2 Pauli(s,s'',1) & = & 0 & 1 \nonumber
                   &   & 1 & 0 \nonumber
  2 Pauli(s,s'',2) & = & 0 & -i \nonumber
                   &   & i &  0 \nonumber
  2 Pauli(s,s'',3) & = & 1 &  0 \nonumber
                   &   & 0 & -1
 \end{eqnarray} }}
    $Amet(y,y'',s,s'') & = & -i Pauli(s,s'',n) E(n,m,m'') Gprimd(m,y) Gprimd(m'',y'')
 \end{eqnarray} }}

 E(n,m,m''):   full antisymetric tensor
 s,s'':        spin indices (1..2)
 y,y'',m,m'',n: metric indices (1..3)
 a,b:         strain indices (1..3)
 Amet and Pauli are complex

PARENTS

      nonlop_pl

CHILDREN

SOURCE

 53 #if defined HAVE_CONFIG_H
 54 #include "config.h"
 55 #endif
 56 
 57 #include "abi_common.h"
 58 
 59 
 60 subroutine metric_so(amet,gprimd,pauli)
 61 
 62  use defs_basis
 63  use m_profiling_abi
 64 
 65 !This section has been created automatically by the script Abilint (TD).
 66 !Do not modify the following lines by hand.
 67 #undef ABI_FUNC
 68 #define ABI_FUNC 'metric_so'
 69 !End of the abilint section
 70 
 71  implicit none
 72 
 73 !Arguments ------------------------------------
 74 !arrays
 75  real(dp),intent(in) :: gprimd(3,3)
 76  real(dp),intent(out) :: amet(2,3,3,2,2),pauli(2,2,2,3)
 77 
 78 !Local variables-------------------------------
 79 !scalars
 80  integer :: iy1,iy2,m1,m2,n
 81 !arrays
 82  real(dp) :: buffer1(3,3,2,2) !,buffer2(3,3,3,3,2,2)
 83 
 84 ! **********************************************************************
 85 
 86 !Fill in Pauli matrices and make them spin matrices:
 87 !Pauli(Re/Im,up,down,coord):
 88  pauli(:,:,:,:)=0.d0
 89  pauli(1,1,2,1)= 1.d0;pauli(1,2,1,1)= 1.d0
 90  pauli(2,1,2,2)=-1.d0;pauli(2,2,1,2)= 1.d0
 91  pauli(1,1,1,3)= 1.d0;pauli(1,2,2,3)=-1.d0
 92  pauli(:,:,:,:)= 0.5d0*pauli(:,:,:,:)
 93 
 94 !Construct the antisymmetric tensor:
 95  amet(:,:,:,:,:)=0.d0
 96  do iy2=1,3
 97    do iy1=1,3
 98      do n=1,3
 99        m1=mod(n ,3)+1    !  n,m1,m2 is an even permutation
100        m2=mod(m1,3)+1
101        amet(1:2,iy1,iy2,1:2,1:2) = amet(:,iy1,iy2,:,:) &
102 &       + pauli(:,:,:,n) &
103 &       *(gprimd(m1,iy1)*gprimd(m2,iy2) &
104 &       -gprimd(m2,iy1)*gprimd(m1,iy2))
105      end do
106    end do
107  end do
108 !amet= -i amet
109  buffer1(:,:,:,:)=-amet(1,:,:,:,:)
110  amet(1,:,:,:,:) = amet(2,:,:,:,:)
111  amet(2,:,:,:,:) =buffer1(:,:,:,:)
112 
113 !DEBUG
114 !!Eventually construct the gradients of Amet wrt strains:
115 !! DAmet(y,y'',a,b,s,s'')= d[Amet(y,y'',s,s'')]/d[strain(a,b)]
116 !!                        -i Pauli(s,s'',n)*
117 !!                          ( E(n,a,m'')*Gprimd(b,y )*Gprimd(m'',y'')
118 !!                           +E(n,m,a )*Gprimd(b,y'')*Gprimd(m ,y ) )
119 !damet(:,:,:,:,:,:,:)=0.d0
120 !do ib=1,3
121 !do ia=1,3
122 !m1=mod(ia,3)+1    !  ia,m1,m2 is an even permutation
123 !m2=mod(m1,3)+1
124 !do iy2=1,3
125 !do iy1=1,3
126 !damet(:,iy1,iy2,ia,ib,:,:) = damet(:,iy1,iy2,ia,ib,:,:) &
127 !&        + (pauli(:,:,:,m2)*gprimd(m1,iy2) &
128 !-pauli(:,:,:,m1)*gprimd(m2,iy2))*gprimd(ib,iy1) &
129 !&        + (pauli(:,:,:,m1)*gprimd(m2,iy1) &
130 !-pauli(:,:,:,m2)*gprimd(m1,iy1))*gprimd(ib,iy2)
131 !end do
132 !end do
133 !end do
134 !end do
135 !! damet= i damet
136 !buffer2(:,:,:,:,:,:)= damet(1,:,:,:,:,:,:)
137 !damet(1,:,:,:,:,:,:)= -damet(2,:,:,:,:,:,:)
138 !damet(2,:,:,:,:,:,:)=buffer2(:,:,:,:,:,:)
139 !! Symetrize damet(:,:,:,a,b,:,:)
140 !damet(:,:,:,1,2,:,:)=0.5d0*(damet(:,:,:,1,2,:,:)+damet(:,:,:,2,1,:,:))
141 !damet(:,:,:,1,3,:,:)=0.5d0*(damet(:,:,:,1,3,:,:)+damet(:,:,:,3,1,:,:))
142 !damet(:,:,:,2,3,:,:)=0.5d0*(damet(:,:,:,2,3,:,:)+damet(:,:,:,3,2,:,:))
143 !damet(:,:,:,2,1,:,:)=damet(:,:,:,1,2,:,:)
144 !damet(:,:,:,3,1,:,:)=damet(:,:,:,1,3,:,:)
145 !damet(:,:,:,3,2,:,:)=damet(:,:,:,2,3,:,:)
146 !ENDDEBUG
147 
148 end subroutine metric_so

TABLE OF CONTENTS

ABINIT/metric_so [ Functions ]