Spectrum in multi-species asymmetric simple exclusion process on a ring

TL;DR

This paper analyzes the spectral properties of a multi-species asymmetric simple exclusion process on a ring, revealing universality class behavior and introducing new spectral dualities through Bethe ansatz techniques.

Contribution

It introduces a novel spectral duality and sector inclusion relations for the multi-species ASEP, and demonstrates Bethe ansatz integrability for the model.

Findings

Relaxation time exponent matches the one-species case.

System belongs to KPZ or EW universality classes depending on symmetry.

New spectral duality and sector inclusion relations derived.

Abstract

The spectrum of Hamiltonian (Markov matrix) of a multi-species asymmetric simple exclusion process on a ring is studied. The dynamical exponent concerning the relaxation time is found to coincide with the one-species case. It implies that the system belongs to the Kardar-Parisi-Zhang or Edwards-Wilkinson universality classes depending on whether the hopping rate is asymmetric or symmetric, respectively. Our derivation exploits a poset structure of the particle sectors, leading to a new spectral duality and inclusion relations. The Bethe ansatz integrability is also demonstrated.