Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process

TL;DR

This paper investigates the dynamical transition in the open-boundary TASEP, providing numerical evidence from DMRG calculations that confirms a transition line distinct from steady-state changes, highlighting differences between static and dynamic phases.

Contribution

It offers the first numerical confirmation of the dynamical transition along the de Gier-Essler line in TASEP using DMRG, contrasting with previous difficulties in Monte Carlo detection.

Findings

DMRG provides clear evidence of the dynamical transition

Monte Carlo simulations are less effective in detecting the transition

The transition line differs from steady-state phase boundaries

Abstract

We revisit the totally asymmetric simple exclusion process with open boundaries (TASEP), focussing on the recent discovery by de Gier and Essler that the model has a dynamical transition along a nontrivial line in the phase diagram. This line coincides neither with any change in the steady-state properties of the TASEP, nor the corresponding line predicted by domain wall theory. We provide numerical evidence that the TASEP indeed has a dynamical transition along the de Gier-Essler line, finding that the most convincing evidence was obtained from Density Matrix Renormalisation Group (DMRG) calculations. By contrast, we find that the dynamical transition is rather hard to see in direct Monte Carlo simulations of the TASEP. We furthermore discuss in general terms scenarios that admit a distinction between static and dynamic phase behaviour.