Elementary excitations of a system of one-dimensional chiral fermions with short-range interactions

TL;DR

This paper investigates how the excitation spectrum of one-dimensional chiral fermions with short-range interactions varies with the nonlinearity of their dispersion, revealing different excitation types and a dynamic phase transition.

Contribution

It provides a detailed analysis of how dispersion nonlinearity influences elementary excitations and identifies a critical interaction strength causing a phase transition.

Findings

Low-momentum excitations are fermionic quasiparticles and quasiholes for quadratic nonlinearity.

High-momentum excitations are classical waves and solitons.

A critical interaction strength induces a qualitative change in the spectrum.

Abstract

We study general features of the excitation spectrum of a system of one-dimensional chiral spinless fermions with short-range interactions. We show that the nature of the elementary excitations of such a system depends strongly on the nonlinearity of the underlying dispersion of the fermions. In the case of quadratic nonlinearity, the low-momentum excitations are essentially fermionic quasiparticles and quasiholes, whereas the high-momentum ones are classical harmonic waves and solitons. In the case of cubic nonlinearity, the nature of the elementary excitations does not depend on momentum and is determined by the strength of the interactions. At a certain critical value of the interaction strength the excitation spectrum changes qualitatively, pointing to a dynamic phase transition in the system.