Realization of Haldane's Exclusion Statistics in a Model of Electron-Phonon Interactions

TL;DR

This paper presents an integrable one-dimensional electron-phonon interaction model demonstrating Haldane's exclusion statistics, revealing how local interactions can produce purely statistical interactions between particles.

Contribution

It introduces a novel integrable model where local interactions lead to fractional exclusion statistics, a first in such a context.

Findings

Electrons and phonons exhibit fractional statistics in the model.

Decoupling phonons at low temperature simplifies the analysis.

Thermodynamic equations for phonons are derived.

Abstract

We discuss an integrable model describing one-dimensional electrons interacting with two-dimensional anharmonic phonons. In the low temperature limit it is possible to decouple phonons and consider one-dimensional excitations separately. They have a trivial two-body scattering matrix and obey fractional statistics. As far as we know the original model presents the first example of a model with local bare interactions generating purely statistical interactions between renormalized particles. As a by-product we obtain non-trivial thermodynamic equations for the interacting system of two-dimensional phonons.