One-body reduced density matrix of trapped impenetrable anyons in one dimension

TL;DR

This paper investigates the one-body reduced density matrix of one-dimensional impenetrable anyons in a harmonic trap, extending computational methods to obtain both exact numerical and asymptotic analytical results.

Contribution

It extends the determinant and replica methods to analyze the density matrix of trapped impenetrable anyons, providing accurate large-$N$ asymptotic expansions and numerical computations.

Findings

Asymptotic expansion matches numerical results for small $N$

Replica method effectively approximates density matrix

Analytic expressions facilitate understanding of anyonic systems

Abstract

We study the one-body reduced density matrix of a system of $N$ one-dimensional impenetrable anyons trapped by a harmonic potential. To this purpose we extend two methods developed to tackle related problems, namely the determinant approach and the replica method. While the former is the basis for exact numerical computations at finite $N$, the latter has the advantage of providing an analytic asymptotic expansion for large $N$. We show that the first few terms of such expansion are sufficient to reproduce the numerical results to an excellent accuracy even for relatively small $N$, thus demonstrating the effectiveness of the replica method.