Hard Core Bosons on the Triangular Lattice at Zero Temperature: A Series Expansion Study

We use high order linked cluster series to investigate the hard core boson model on the triangular lattice, at zero temperature. Our expansions, in powers of the hopping parameter $t$, probe the spatially ordered `solid’ phase and the transition to a uniform superfluid phase. At the commensurate fillings $n=1/3, 2/3$welocateaquantumphasetransitionpointat$(t/V)_c\simeq 0.208(1)$, in good agreement with recent Monte Carlo studies. At half-filling ($n=1\mathrm{/}2$) we find evidence for a solid phase, which persists to $t\mathrm{/}V\simeq 0.06$.