Symmetries in zero and finite center of mass momenta excitons

Exciton calculations often face computational bottlenecks due to the need for diagonalization of large-scale Bethe-Salpeter Equation (BSE) Hamiltonians. This problem becomes more severe for fine exciton center-of-mass (COM) momentum sampling, where we need to diagonalise Hamiltonians for many exciton COM momenta. We use a crystal symmetry-based approach to reduce this computational cost. We implement the rotation of finite COM exciton wavefunctions based on crystal symmetries from a calculation of exciton wavefunctions on the irreducible Brillouin zone. In addition, we introduce a symmetry-adapted basis to block-diagonalize the BSE Hamiltonian at zero exciton COM momentum, further reducing the computational costs. This method enables efficient calculation of the quantities like exciton-phonon couplings and exciton spectra.