Fermionic behavior of ideal anyons

TL;DR

This paper establishes bounds on the ground-state energy of a two-dimensional ideal anyon gas, revealing fermionic behavior and extending Lieb-Thirring inequalities to all anyons except bosons.

Contribution

It provides the first rigorous bounds on the energy of ideal anyons, demonstrating fermionic characteristics and generalizing Lieb-Thirring inequalities.

Findings

Bounds on ground-state energy scale extensively with particle number

Energy bounds are linear in the statistics parameter 

Lieb-Thirring inequalities are extended to all anyons except bosons

Abstract

We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter $\alpha$. The lower bounds extend to Lieb-Thirring inequalities for all anyons except bosons.