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Codes for constructing matrix of Hamiltonion of 2D square Tight-bonding model

  1. Aug 13, 2010 #1
    Does anyone know how to write codes for constructing the matrix of Hamiltonion of 2D square Tight-bonding model. Then diagonalize it.
    Any language is OK. (Fortran is best)
  2. jcsd
  3. Aug 23, 2010 #2

    This program shows the principle of diagonalizing a
    matrix in fortran, using a 2D geometry. To compile, write
    gfortran -llapack 2D.f90
    then write ./a.out to run the program
    Or ifort -llapack 2D.f90

    Code (Text):
    module shared !every function and routine which
    implicit none !includes the module shared can use its
    real*8, allocatable :: Hdiag(:,:),eigenvalues(:)  !variables
    end module shared

    program diag
    use shared !now the program diag knows about Hdiag and eigenvalues
    implicit none !this makes sure one has do define everything explicitly
    integer :: nsize !size of the matrix to be diagonalized
    integer :: i,j,icount,jcount,norb
    integer :: i1,i2,j1,j2
    real*8 :: v

    norb = 5 !size of system

    nsize = norb*norb !size of hamiltonian

    allocate(Hdiag(nsize,nsize)) !This is the matrix to be diagonalized
    allocate(eigenvalues(nsize)) !after diagonalization, this vector
    !contains the eigenvalues

    v = -1.0 !this is the hopping parameter

    !Now we construct the hamiltonian, and we do that by first looping over
    !j, and then i. This are non-periodic boundary conditions.
    icount = 0
    jcount = 0
    do i1=1,norb
    do j1=1,norb
       jcount = 0
       icount = icount + 1
       do i2=1,norb
       do j2=1,norb
          jcount = jcount + 1
          if (abs(i1-i2) + abs(j1-j2) == 1)Hdiag(icount,jcount) = v !if distance == 1, put hopping parameter = v
          write(11,*)'hop(',icount,jcount,')=',Hdiag(icount,jcount) !this prints the hamiltonian to disc
       end do                                
       end do
    end do
    end do

    call diagonalize(nsize) !now Hdiag will be diagonalized.
    !After diagonalization, Hdiag(:,:) will contain the eigenvectors,
    !Where Hdiag(:,1) is the first eigenvector, Hdiag(:,2) the second and so on
    !and eigenvalues(1) will contain the eigenvalue corresponding to
    !eigenvector 1, and so on.

    do i=1,nsize
    write(*,*)'eigenvalue:',i,eigenvalues(i) !writing eigenvalues to screen
    end do
    end program diag !program is finished

    subroutine diagonalize(ndiag) !Diagonalizes the matrix Hdiag
    use shared
    implicit none
    real*8,  allocatable :: work(:)
    integer, allocatable :: iwork(:)
    character job, uplo
    external dsyevd
    integer nmax, lda, lwork, liwork, info,ndiag
    call dsyevd(job,uplo,ndiag,Hdiag,lda,eigenvalues,work,lwork,iwork,liwork,info)
    if (info > 0) then
       write (*,*) 'failure to converge.'
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