$U(1)$ Fermi liquid theory - A Fermi liquid state that supports exclusion statistics

TL;DR

This paper introduces a novel $U(1)$ Fermi liquid theory where quasi-particle momentum depends on occupation numbers, leading to exclusion statistics and deviations from traditional Fermi liquid behavior.

Contribution

It extends Landau Fermi liquid theory by incorporating momentum-dependent interactions that produce exclusion statistics, a feature not present in standard models.

Findings

Supports exclusion statistics in a Fermi liquid framework

Quasi-particles are not adiabatically connected to bare fermions

May violate Luttinger theorem

Abstract

We propose in this paper an effective low-energy theory for interacting fermion systems which supports exclusion statistics. The theory can be viewed as an extension of Landau Fermi liquid theory where besides quasi-particle energy $\xi_{\mathbf{k}}$, the kinetic momentum $\mathbf{k}$ of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum ($k$)-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is studied where we show that the state (which we call $U(1)$-Fermi liquid state) has Fermi-liquid like properties except that the quasi-particles are {\em not} adiabatically connected to bare fermions in the system and the state may not satisfy Luttinger theorem.