Symmetry considerations in exact diagonalization: spin-1/2 pyrochlore magnets

We describe how the methods of group theory (symmetry) are used to optimize the problem of exact diagonalization of a quantum system on a 16-site pyrochlore lattice. By analytically constructing a complete set of symmetrized states, the Hamiltonian can be completely block-diagonalized. As an example, we consider a spin-1/2 system with nearest-neighbour exchange interactions. We present the energy spectrum of a small system for a range of model parameters in the vicinity of the spin ice phase.