Quantum entanglement of particles on a ring with fractional statistics

TL;DR

This paper explores how quantum entanglement in one-dimensional anyonic systems varies with interaction strength and fractional statistics, revealing the influence of the anyonic phase on entanglement entropy.

Contribution

It provides a detailed analysis of entanglement entropy in anyonic systems using Bethe-ansatz, highlighting the effects of fractional statistics and interaction strength.

Findings

Entanglement entropy increases with interaction strength.

Statistical parameter renormalizes effective interaction and adds an anyonic phase.

Distinct entanglement behavior observed for different fractional statistics.

Abstract

In this paper we investigate the von Neumann entropy in the ground state of one-dimensional anyonic systems with the repulsive interaction. Based on the Bethe-ansatz method, the entanglement properties for the arbitrary statistical parameter ($0\leq\kappa\leq1$) are obtained from the one-particle reduced density matrix in the full interacting regime. It is shown that the entanglement entropy increases with the increase in the interaction strength and statistical parameter. The statistic parameter affects the entanglement properties from two aspects: renormalizing of the effective interaction strength and introducing an additional anyonic phase. We also evaluate the entanglement entropy of hard-core anyons for different statistical parameters in order to clarify solely the effect induced by the anyonic phase.