Hidden symmetries in the asymmetric exclusion process

TL;DR

This paper investigates hidden symmetries in the spectral properties of the asymmetric exclusion process, revealing higher-order degeneracies and suggesting the existence of underlying symmetries beyond known ones, especially in large systems.

Contribution

It uncovers higher-order spectral degeneracies in ASEP and links them to hidden symmetries explained via Bethe Ansatz, extending understanding of the model's symmetry structure.

Findings

Higher-order degeneracies increase with system size

Hidden symmetries are suggested by spectral degeneracies

Bethe Ansatz explains the degeneracy patterns

Abstract

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However, we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies become generic in the limit of very large systems. This behaviour can be explained by the Bethe Ansatz and suggests the presence of hidden symmetries in the model. Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe Ansatz.