Supersolidity, entropy, and frustration: t-t -V model of hard-core bosons on the triangular lattice

We study the properties of t-t -V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1 /2 XXZ model in a field, we determine the phase diagram of the t-V model where the supersolid characterized by the ordering pattern x ,x ,−2x “ferrimagnetic” or SS A is a ground state for chemical potential 3V. By turning on either temperature or t at half filling =3V , we find a first order transition from SS A to the elusive supersolid characterized by the x ,−x ,0 ordering pattern “antiferromagnetic” or SS C . In addition, we find a large region where a superfluid phase becomes a solid upon increasing temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.