Equilibration in a chiral Luttinger liquid

TL;DR

This paper investigates the equilibration processes in a chiral Luttinger liquid with finite-range interactions, revealing temperature-dependent scaling laws for relaxation rates in different regimes.

Contribution

It introduces a duality mapping to analyze equilibration in chiral Luttinger liquids and derives new temperature-dependent scaling laws for relaxation rates.

Findings

Equilibration rate scales as T^5 at high temperatures.

Equilibration rate scales as T^{14} at low temperatures.

Hot particle relaxation scales as k^7 T^7.

Abstract

We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with non-linear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature $T$ or weakly interacting bosons at high $T$. We calculate the equilibration rate which is found to scale with temperature as $T^5$ and $T^{14}$ in the high-temperature ("bosonic") and the low-temperature ("fermonic") regimes, respectively. The relaxation rate of a hot particle with the momentum $k$ in the fermonic regime scales as $k^7T^7$.