Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics

TL;DR

This paper extends Lieb-Thirring inequalities to particles with intermediate and fractional statistics in one and two dimensions, providing new bounds based on a local exclusion principle applicable to anyons and similar particles.

Contribution

It derives novel Lieb-Thirring inequalities for intermediate and fractional statistics, broadening the understanding of quantum many-body systems beyond bosons and fermions.

Findings

New Lieb-Thirring inequalities for intermediate statistics in 1D

Application of inequalities to Lieb-Liniger and Calogero-Sutherland models

Establishment of a local exclusion principle for generalized exchange statistics

Abstract

In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider applications of a recent Lieb-Thirring inequality for anyons in two dimensions, and derive new Lieb-Thirring inequalities for intermediate statistics in one dimension with implications for models of Lieb-Liniger and Calogero-Sutherland type. These inequalities follow from a local form of the exclusion principle valid for such generalized exchange statistics.