A three-site Bose-Fermi ring with a few atoms

We investigate a three-site ring system with a small number of ultracold, quantum degenerate bosons and fermions. By means of the exact diagonalization of the Bose-Fermi-Hubbard Hamiltonian, we show that the symmetry of the ground state configuration is a function of both the boson-boson and the inter-species interaction in the system. The phase diagram of the system, constructed by computing the exact two-body spatial correlations, reveals nontrivial insulating phases that exist even in the strong bosonic tunnelling limit and for incommensurate filling of bosons. These insulating phases are due to the inter-species interactions in the system and are not necessarily accompanied by the suppression of the particle number fluctuations.