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 mu>3V. By turning on either temperature or t(') at half filling (mu=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.