Quantum liquids of particles with generalized statistics

TL;DR

This paper develops a phenomenological Landau Fermi liquid-like theory for quantum liquids of particles obeying fractional exclusion statistics, analyzing their thermodynamic and transport properties and revealing non-Fermi liquid behaviors.

Contribution

It introduces a new framework for describing quantum liquids with generalized statistics, extending Fermi liquid theory to fractional exclusion statistics in multiple dimensions.

Findings

Low temperature properties mimic Fermi liquids with statistics-dependent coefficients.

Explicit realization of non-Fermi liquid Lorentz ratios in higher dimensions.

Theoretical consistency confirmed via sum rules and compressibility calculations.

Abstract

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low temperature quantities have the same temperature dependences as for the Fermi liquid, with the coefficients depending on the statistics parameter. The novel quantum liquids provide explicit realization of systems with a non-Fermi liquid Lorentz ratio in two and more dimensions. Consistency of the theory is verified by deriving the compressibility and $f$-sum rules.