Spectral Degeneracies in the Totally Asymmetric Exclusion Process

TL;DR

This paper investigates the spectrum of the Markov matrix in TASEP, revealing unexpected high-order degeneracies explained by hidden symmetries and Bethe Ansatz, suggesting a large underlying invariance group.

Contribution

It uncovers hidden symmetries in TASEP's spectrum and provides combinatorial formulas for degeneracy orders, supported by numerical validation.

Findings

High-order degeneracies in TASEP spectrum explained by hidden symmetries

Derivation of combinatorial formulas for degeneracy and multiplet counts

Numerical results confirm theoretical predictions

Abstract

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the corresponding number of multiplets are derived and compared with numerical results obtained from exact diagonalisation of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group. Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.