Universal correlations of trapped one-dimensional impenetrable bosons

TL;DR

This paper derives universal asymptotic expressions for the one-body density matrix of finite-size one-dimensional impenetrable bosons, revealing oscillating terms akin to Friedel oscillations due to strong correlations.

Contribution

It introduces a modified Replica Method to analytically compute the asymptotic behaviour of the density matrix in finite geometries, highlighting universality of oscillations.

Findings

Explicit expressions for oscillating terms in the density matrix

Identification of universal Friedel-like oscillations

Demonstration of strong short-range correlation effects

Abstract

We calculate the asymptotic behaviour of the one body density matrix of one-dimensional impenetrable bosons in finite size geometries. Our approach is based on a modification of the Replica Method from the theory of disordered systems. We obtain explicit expressions for oscillating terms, similar to fermionic Friedel oscillations. These terms are universal and originate from the strong short-range correlations between bosons in one dimension.