We numerically demonstrate that a supersolid phase exists in a frustrated hard-core boson system on a triangular lattice over a wide range of interaction strength. In the infinite repulsion (Ising) limit, we establish a mapping to the same problem with unfrustrated hopping, which connects the supersolid to the known results in that case. The weak superfluidity can be destroyed or strongly enhanced by a next-nearest-neighbor hopping term, which provides valuable information for experimental realization of a supersolid phase on optical lattice. A phase diagram for the frustrated anisotropic Heisenberg model on triangular lattice is also established.
We study the properties of $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}V$ 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 $t\text{\ensuremath{-}}V$ model where the supersolid characterized by the ordering pattern $(x,x,\ensuremath{-}2{x}^{\ensuremath{'}})$ (``ferrimagnetic'' or SS
A) is a ground state for chemical potential $\ensuremath{\mu}>3V$. By turning on either temperature or ${t}^{\ensuremath{'}}$ at half filling $(\ensuremath{\mu}=3V)$, we find a first order transition from SS
A to the elusive supersolid characterized by the $(x,\ensuremath{-}x,0)$ 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.