Relaxation times in the ASEP model using a DMRG method

TL;DR

This paper uses a DMRG method to compute relaxation times in the TASEP model, confirming the domain wall theory for large systems and recovering the KPZ dynamical exponent in the maximal current phase.

Contribution

It introduces a DMRG approach to analyze relaxation times in TASEP, enabling larger system sizes and validating theoretical predictions.

Findings

Domain wall theory accurately predicts relaxation times for large systems.

KPZ dynamical exponent z=3/2 is confirmed in the maximal current phase.

Method extends analysis beyond the domain wall approach's validity.

Abstract

We compute the largest relaxation times for the totally asymmetric exclusion process (TASEP) with open boundary conditions with a DMRG method. This allows us to reach much larger system sizes than in previous numerical studies. We are then able to show that the phenomenological theory of the domain wall indeed predicts correctly the largest relaxation time for large systems. Besides, we can obtain results even when the domain wall approach breaks down, and show that the KPZ dynamical exponent $z=3/2$ is recovered in the whole maximal current phase.