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.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.

arXiv:1910.11365National Science ReviewFeb 21, 20227 citations

q-Deformation and Free Statistics for Interaction of a Field and a Particle

Sergei Vladimirovich Kozyrev

Abstract Emerging of free (or quantum Boltzmann) statistics for a model of quantum particle interacting with quantum field is described in the stochastic limit without dipole approximation. The quantum field is considered in a Gaussian (for example temperature) state. Entangled operators which describe interaction of the field and the particle satisfy the $q$ -deformed relations which in the stochastic limit generate free statistics.Abstract Emerging of free (or quantum Boltzmann) statistics for a model of quantum particle interacting with quantum field is described in the stochastic limit without dipole approximation. The quantum field is considered in a Gaussian (for example temperature) state. Entangled operators which describe interaction of the field and the particle satisfy the $$q$$ -deformed relations which in the stochastic limit generate free statistics.

arXiv:2001.01602Physics of Particles and NucleiJul 1, 20200 citations

Interacting Particles as neither Bosons nor Fermions: A Microscopic Origin for Fractional Exclusion Statistics

Kazumoto Iguchi, Bill Sutherland

We study a quantum liquid of particles interacting via a long-ranged two-body potential in three dimensions where the original particles are supposed to be either bosons or fermions. We show that such liquids exhibit the nature of a quantum liquid with fractional exclusion statistics. In both quantum liquids enlarged pseudo-Fermi surfaces are formed from bosons and fermions, although with different excitations. Hence, we conclude that the microscopic origin of exclusion statistics comes from the nature of long-ranged two-body interactions between the particles.We study a quantum liquid of particles interacting via a long-ranged two-body potential in three dimensions where the original particles are supposed to be either bosons or fermions. We show that such liquids exhibit the nature of a quantum liquid with fractional exclusion statistics. In both quantum liquids enlarged pseudo-Fermi surfaces are formed from bosons and fermions, although with different excitations. Hence, we conclude that the microscopic origin of exclusion statistics comes from the nature of long-ranged two-body interactions between the particles.

Physical Review LettersSep 25, 200011 citations

q

-deformed relations which in the stochastic limit generate free statistics.