The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics

TL;DR

This paper investigates the low-energy behavior of a one-dimensional interacting anyon gas, revealing how its statistical parameter influences exclusion statistics and interpolates between bosonic and fermionic behaviors, with implications for quantum many-body systems.

Contribution

It demonstrates how the anyonic parameter and interaction strength induce Haldane exclusion statistics, including beyond Fermi statistics, providing a detailed analysis of various coupling regimes.

Findings

Anyonic parameter interpolates between bosons and fermions.

Exclusion statistics parameter $ ext{α}$ can exceed one.

Universal role of $ ext{α}$ in dispersion relations.

Abstract

The low energy properties of the one-dimensional anyon gas with $\delta$-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter $\alpha$ is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of $\alpha$ in the dispersion relations.