Trap-size scaling in confined particle systems at quantum transitions

TL;DR

This paper develops a trap-size scaling theory for quantum phase transitions in confined particle systems, validated through exact and numerical results on the XY chain and Bose-Hubbard model relevant to cold atomic gases.

Contribution

It introduces a new trap-size scaling framework for quantum transitions and applies it to specific models, providing exact and numerical insights.

Findings

Validated trap-size scaling in XY chain and Bose-Hubbard models

Provided exact and numerical results for quantum phase transitions

Relevant for cold atomic gases in optical lattices

Abstract

We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We discuss trap-size scaling at the Mott insulator to superfluid transition in the Bose-Hubbard model. We present exact and accurate numerical results for the XY chain and for the low-density Mott transition in the hard-core limit of the one-dimensional Bose-Hubbard model. Our results are relevant for systems of cold atomic gases in optical lattices.