Ground state of the hard-core Bose gas on lattice I. Energy estimates

TL;DR

This paper improves the upper bound on the ground state energy of a hard-core Bose gas on lattices by employing variational methods and large deviation principles, providing tighter energy estimates for the system.

Contribution

It introduces a novel variational approach and utilizes large deviation principles to refine the upper bound on the ground state energy for the hard-core Bose gas.

Findings

Derived a smaller variational upper bound on the energy per site.

Utilized large deviation principles for the Ising model energy.

Enhanced understanding of the ground state properties of lattice boson systems.

Abstract

We investigate the properties of the ground state of a system of interacting bosons on regular lattices with coordination number $k\geq 2$. The interaction is a pure, infinite, on-site repulsion. Our concern is to give an improved upper bound on the ground state energy per site. For a density $\rho$ a trivial upper bound is known to be $-k\rho(1-\rho)$. We obtain a smaller variational bound within a reasonably large family of trial functions. The estimates make use of a large deviation principle for the energy of the Ising model on the same lattice.