Interaction-induced particle-hole symmetry breaking and fractional exclusion statistics

Xibo Zhang; Yang-Yang Chen; Longxiang Liu; Youjin Deng; Xiwen Guan

doi:10.1093/nsr/nwac027

Interaction-induced particle-hole symmetry breaking and fractional exclusion statistics

Natl Sci Rev. 2022 Feb 24;9(12):nwac027. doi: 10.1093/nsr/nwac027. eCollection 2022 Dec.

Authors

Xibo Zhang^{1

2

3}, Yang-Yang Chen^{4

5}, Longxiang Liu⁶, Youjin Deng^{6

7}, Xiwen Guan^{4

8}

Affiliations

¹ International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
² Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
³ Beijing Academy of Quantum Information Sciences, Beijing 100193, China.
⁴ State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China.
⁵ Institute of Modern Physics, Northwest University, Xi'an 710127, China.
⁶ Chinese Academy of Sciences Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230326, China.
⁷ MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China.
⁸ Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia.

Abstract

Quantum statistics plays a fundamental role in the laws of nature. Haldane fractional exclusion statistics (FES) generalizes the Pauli exclusion statistics, and can emerge in the properties of elementary particles and hole excitations of a quantum system consisting of conventional bosons or fermions. FES has a long history of intensive studies, but its simple realization in interacting physical systems is rare. Here we report a simple non-mutual FES that depicts the particle-hole symmetry breaking in interacting Bose gases at a quantum critical point. We show that the FES distribution directly comes from particle-hole symmetry breaking. Based on exact solutions, quantum Monte Carlo simulations and experiments, we find that, over a wide range of interaction strengths, the macroscopic physical properties of these gases are determined by non-interacting quasi-particles that obey non-mutual FES of the same form in one and two dimensions. Whereas strongly interacting Bose gases reach full fermionization in one dimension, they exhibit incomplete fermionization in two dimensions. Our results provide a generic connection between interaction-induced particle-hole symmetry breaking (depicted by FES) and macroscopic properties of many-body systems in arbitrary dimensions. Our work lays the groundwork for using FES to explore quantum criticality and other novel many-body phenomena in strongly correlated quantum systems.

Keywords: fractional exclusion statistics; interaction; particle-hole symmetry breaking; quantum statistics; strongly correlated quantum materials.