Symmetry-driven compression of the set of states of a Hubbard ring

We present a method of the reduction of the system size driven by the system symmetry, as applied to a quantum system. Here we analyse the state space formed by possible states of a ring of atoms, within the single-band Hubbard model in the atomic limit. We show that all states may be divided into some number of classes, which allows for a significant reduction of the system size.