Spin wave theory for interacting hardcore bosons on cubic lattices: a comparative study

TL;DR

This paper develops a spin wave theory for interacting hardcore bosons on cubic lattices, comparing its predictions with Quantum Monte Carlo results to understand phase boundaries and transitions.

Contribution

It introduces a spin wave theory for interacting hardcore bosons on cubic lattices and compares its thermodynamic predictions with stochastic series expansion results.

Findings

Good agreement between SWT and SSE for small repulsions on cubic lattices.

Discrepancies between SWT and SSE at strong repulsions on square lattices.

Phase boundaries identified for MI, SF, and NS phases.

Abstract

Motivated by excellent comparisons of spin wave theory (SWT) with Quantum Monte Carlo (QMC) calculations of non-interacting hardore bosons (Bernardet et al.) and superlattices (Hen et al.), we develop an SWT for interacting hardcore bosons on a d-dimensional cubic lattice at zero temperature and compare thermodynamical properties with results of Stochastic Series Expansions (SSE): there is good comparison between SWT and SSE results for the simple cubic lattice at small repulsive strengths but differences arise between the results of the two approaches for the square lattice at strong repulsions. The boundaries of the three phases - Mott insulating (MI), superfluid (SF) and N\'{e}el solid (NS) - can be readily estimated from calculations of particle density, signalling either a first order (SF <--> NS) or second order transition (MI <--> SF). Comparison is made with results of the Bethe ansatz in one dimension and QMC in two dimensions.