Local exclusion principle for identical particles obeying intermediate and fractional statistics

TL;DR

This paper establishes a local exclusion principle for particles with fractional statistics, deriving kinetic energy bounds and implications for models like Lieb-Liniger and Calogero-Sutherland, especially for anyon gases.

Contribution

It introduces a local exclusion principle for fractional statistics particles and derives energy bounds relevant to specific quantum models.

Findings

Bounds for kinetic energy in fractional statistics systems

Implications for Lieb-Liniger and Calogero-Sutherland models

Lower energy bounds for anyon gases with odd numerator fractions

Abstract

A local exclusion principle is observed for identical particles obeying intermediate/fractional exchange statistics in one and two dimensions, leading to bounds for the kinetic energy in terms of the density. This has implications for models of Lieb-Liniger and Calogero-Sutherland type, and implies a non-trivial lower bound for the energy of the anyon gas whenever the statistics parameter is an odd numerator fraction. We discuss whether this is actually a necessary requirement.