Universal properties of hard-core bosons confined on one-dimensional lattices

TL;DR

This paper provides an exact analysis of hard-core bosons in one-dimensional lattices, revealing universal behaviors in their density matrix and natural orbital occupations, independent of confining potentials.

Contribution

It offers an exact theoretical framework for understanding the large-distance behavior and natural orbital occupations of hard-core bosons in 1D lattices, highlighting their universal properties.

Findings

Universal decay of the one-particle density matrix

Occupation of lowest natural orbital in the thermodynamic limit

Finite-size effects on momentum distribution

Abstract

Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain the large distance behavior of the one-particle density matrix, and show how it determines the occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation $\lambda_{\eta}$ of the natural orbitals for large-$\eta$ at low densities. Both quantities show universal behavior independently of the confining potential. Finite-size corrections and the momentum distribution function for finite systems are also analyzed.