Phase diagram of the t-J model on a honeycomb lattice

We investigate the phase diagram for the t-J model on a two-dimensional honeycomb structure at low electronic densities. The phase diagram as a function of the interaction strength, J, consists of three phases, viz. a gas of electrons for 0 <= J < 2t, a gas of pairs for 2t <= J < 3.29t, and a fully phase-separated state for J > 3.29t. Further, we rigorously prove that a gas of electrons start forming pairs at J=2t and the value is the same for any bipartite lattice in any dimension. We have elaborately explored the possibilities of formation of bigger clusters, i.e., bound states of three, four, and six electrons by performing exact diagonalization and perturbative analysis and ruled out formation of such clusters in the phase diagram.