Sublattice coding algorithm and distributed memory parallelization for large-scale exact diagonalizations of quantum many-body systems

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in exact diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of symmetry-adapted wave functions. Moreover, a parallelization scheme for the Hamiltonian-vector multiplication in the Lanczos procedure for distributed memory machines avoiding load-balancing problems is proposed. We demonstrate that using these methods low-energy properties of systems of up to 50 spin-$1/2$ particles can be successfully determined.