Extrapolation methods and Bethe ansatz for the asymmetric exclusion process

Abstract

The one-dimensional asymmetric simple exclusion process (ASEP), where N hard-core particles hop forward with rate 1 and backward with rate , is considered on a periodic lattice of L site. Using KPZ universality and previous results for the totally asymmetric model , precise conjectures are formulated for asymptotics at finite density of ASEP eigenstates close to the stationary state. The conjectures are checked with high precision using extrapolation methods on finite size Bethe ansatz numerics. For weak asymmetry , double extrapolation combined with an integer relation algorithm gives an exact expression for the spectral gap up to 10th order in the asymmetry.