Dynamical transition in the open-boundary totally asymmetric exclusion process

We revisit the totally asymmetric simple exclusion process (TASEP) with open boundaries, 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 with the corresponding line predicted by the 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 the density matrix renormalization group calculations. By contrast, we find that the dynamical transition is rather difficult to see in direct Monte Carlo simulations of the TASEP. We furthermore discuss in general terms scenarios that admit a distinction between the static and dynamic phase behaviour.