atom.umat.dat

Introduction

The atom.umat.dat file contains the general (four-fermions) Coulomb interaction matrix. Only the non-zero matrix elements (> 1.0E-10) are outputted.

Format

The format of the atom.umat.dat file is as follows:

column 1: orbital index $\alpha$, integer

column 2: orbital index $\beta$, integer

column 3: orbital index $\gamma$, integer

column 4: orbital index $\delta$, integer

column 5: Elements of general Coulomb matrix $U_{\alpha\beta\gamma\delta}$, real part, double precision

column 6: Elements of general Coulomb matrix $U_{\alpha\beta\gamma\delta}$, imaginary part, double precision

Note

In the atom.umat.dat file, we adopt the following orbital sequence: $1\uparrow$, $2\uparrow$, $3\uparrow$, $\cdots$, $1\downarrow$, $2\downarrow$, $3\downarrow$, $\cdots$ In other words, the spin up part is always before the spin down part.

Code

The corresponding Fortran code block for the writing of the atom.umat.dat file is as follows:

! open file atom.umat.dat to write
     open(mytmp, file='atom.umat.dat', form='formatted', status='unknown')

! write the header
     write(mytmp,'(75a1)') dash ! dashed line
     write(mytmp,'(a)') '# i | j | k | l | umat_real | umat_imag'
     write(mytmp,'(75a1)') dash ! dashed line

! write the data, only the non-zero elements are outputed
! note: we do not change the spin sequence here
     do i=1,norbs
         do j=1,norbs
             do k=1,norbs
                 do l=1,norbs
                     if ( abs( umat(i,j,k,l) ) > epst ) then
                         write(mytmp,'(4i6,2f16.8)') i, j, k, l, umat(i,j,k,l)
                     endif ! back if ( abs( umat(i,j,k,l) ) > epst ) block
                 enddo ! over l={1,norbs} loop
             enddo ! over k={1,norbs} loop
         enddo ! over j={1,norbs} loop
     enddo ! over i={1,norbs} loop

! close data file
     close(mytmp)

In general, the Coulomb interaction matrix is complex.

See also solver.umat.in for more details.