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

TL;DR

This study uses high-order series expansions to analyze phase transitions in hard core bosons on a triangular lattice at zero temperature, identifying critical points and phases with high precision.

Contribution

It provides detailed series expansion results for phase boundaries and critical points, improving understanding of quantum phase transitions in this model.

Findings

Quantum phase transition at (t/V)_c ≈ 0.208 at n=1/3, 2/3

Solid phase persists up to t/V ≈ 0.06 at half-filling

Agreement with recent Monte Carlo results

Abstract

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 $n=1/3, 2/3$ we locate a quantum phase transition point at $(t/V)_c\simeq 0.208(1)$, in good agreement with recent Monte Carlo studies. At half-filling ($n=1/2$) we find evidence for a solid phase, which persists to $t/V\simeq 0.06$.