Exclusion bounds for extended anyons

TL;DR

This paper develops a rigorous mathematical framework for understanding the spectral properties of extended anyons, revealing new inequalities and energy estimates that depend on the particles' statistics parameter.

Contribution

It introduces magnetic Hardy inequalities and exclusion principles for extended anyons, advancing the theoretical understanding of their many-body spectral behavior.

Findings

Derived many-body magnetic Hardy inequalities.

Established local exclusion principles for extended anyons.

Provided energy estimates across all parameters.

Abstract

We introduce a rigorous approach to the many-body spectral theory of extended anyons, i.e. quantum particles confined to two dimensions that interact via attached magnetic fluxes of finite extent. Our main results are many-body magnetic Hardy inequalities and local exclusion principles for these particles, leading to estimates for the ground-state energy of the anyon gas over the full range of the parameters. This brings out further non-trivial aspects in the dependence on the anyonic statistics parameter, and also gives improvements in the ideal (non-extended) case.