Ground states of hard-core bosons in one dimensional periodic potentials

TL;DR

This paper derives exact ground states for one-dimensional hard-core bosons in periodic potentials, revealing conditions for Mott insulator and metallic phases, and discusses the absence of superfluidity in such systems.

Contribution

It provides an exact solution for the ground states of hard-core bosons in 1D periodic potentials and analyzes their phase behavior, including Mott insulator and metal phases.

Findings

Boson system is a Mott insulator when N is commensurate with M.

Energy gap equals the single-particle band gap.

System may lack a superfluid phase in 1D.

Abstract

With Girardeau's Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one dimensional periodic potential. The analysis of these ground states shows that when the number of bosons $N$ is commensurate with the number of wells $M$ in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when $N$ is not commensurate with $M$, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in terms of Landau's criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.