initialize_excit_table Subroutine

    subroutine initialize_excit_table()
        ! This cannot be a member of the lattice class because that would introduce
        ! a circulat dependency on get_offdiag_helement_k_sp_hub
        integer :: a, b, i, j, ex(2, 2)
        ! nI is not needed anywhere, it is a redundant argument in the k_space_hubbard module
        integer :: nI(2)
        real(dp) :: matEL

        ! the buffer for excitations is (number of states)^3
        ! strictly speaking, we do not need to distinguish spin orbs here for simple hubbard
        ! but for transcorrelated, it might matter
        if (allocated(excit_cache)) deallocate(excit_cache)

        allocate(excit_cache(nbasis, nbasis, nbasis))
        ! loop over all pairs of orbitals
        do i = 1, nbasis
            do j = 1, nbasis
                nI = [i, j]
                ex(1, :) = [i, j]
                ! and for each, check all possible excitations
                do a = 1, nbasis
                    matEl = 0.0_dp
                    if (a /= i .and. a /= j) then
                        b = get_orb_from_kpoints(i, j, a)
                        if (b /= a .and. b /= i .and. b /= j) then
                            ex(2, :) = [a, b]
                            matEl = abs(get_offdiag_helement_k_sp_hub(nI, ex, .false.))
                        end if
                    end if
                    ! most excitations will have a finite amplitude, so store all
                    excit_cache(i, j, a) = matEl
                end do
            end do
        end do

    end subroutine initialize_excit_table