Evidences for interaction-induced Haldane fractional exclusion statistics in one and higher dimensions

TL;DR

This paper provides evidence that strongly interacting Bose gases in one and two dimensions exhibit fractional exclusion statistics, allowing their thermodynamic behavior to be described by non-interacting particles with FES, bridging interactions and statistics.

Contribution

It demonstrates that repulsively interacting Bose gases obey FES across dimensions, establishing an interaction-to-FES mapping and revealing the statistical nature of particle-hole symmetry breaking.

Findings

Thermodynamic properties match those of FES particles.

Full fermionization in 1D, incomplete in 2D.

Provides a new framework for understanding correlated systems.

Abstract

Haldane fractional exclusion statistics (FES) has a long history of intense studies, but its realization in physical systems is rare. Here we study repulsively interacting Bose gases at and near a quantum critical point, and find evidences that such strongly correlated gases obey simple non-mutual FES over a wide range of interaction strengths in both one and two dimensions. Based on exact solutions in one dimension, quantum Monte Carlo simulations and experiments in both dimensions, we show that the thermodynamic properties of these interacting gases, including entropy per particle, density and pressure, are essentially equivalent to those of non-interacting particles with FES. Accordingly, we establish a simple interaction-to-FES mapping that reveals the statistical nature of particle-hole symmetry breaking induced by interaction in such quantum many-body systems. Whereas strongly interacting Bose gases reach full fermionization in one dimension, they exhibit incomplete fermionization in two dimensions. Our results open a route to understanding correlated interacting systems via non-interacting particles with FES in arbitrary dimensions.