Exclusion statistics and strongly correlated electron systems

Masatoshi Imada, Norio Kawakami, Hiroyuki Shiba +1 more

T Fukui, N Kawakami

Transport properties of the multicomponent quantum many-body systems obeying Haldane's fractional exclusion statistics are studied in one dimension. By computing the finite-size spectrum under twisted boundary conditions, we explicitly express the conductivity and conductance in terms of statistical interactions. Through this analysis, the effective charge and effective mass for collective excitations are determined. We apply the results for l/r 2 quantum systems as well as for correlated electron systems.

Andrea Di Ciolo, Adolfo Avella

Xibo Zhang, Yang-Yang Chen, Longxiang Liu +2 more

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.

Pavel V. Shevchenko

Murray T. Batchelor, Xin Guan

We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one-dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting anyons, including the strongly interacting one-dimensional Bose gas.