Lifted TASEP: long-time dynamics,generalizations, and continuum limit

TL;DR

This paper studies the spectral properties, continuum limit, and generalizations of the lifted TASEP, revealing new insights into its dynamics, integrability, and connections to Monte Carlo algorithms, with implications for understanding relaxation times and stationary states.

Contribution

It introduces the continuum limit of lifted TASEP, generalizes it to models with non-trivial Boltzmann stationary states, and links these to Monte Carlo methods and integrability.

Findings

Spectral analysis explains relaxation time scaling discrepancies.

Continuum limit remains integrable and connects to event-chain Monte Carlo.

Tuning parameters achieves polynomial speedup in convergence to steady state.

Abstract

We investigate the lifted TASEP and its generalization, the GL-TASEP. We analyze the spectral properties of the transition matrix of the lifted TASEP using its Bethe ansatz solution, and use them to determine the scaling of the relaxation time (the inverse spectral gap) with particle number. The observed scaling with particle number was previously found to disagree with Monte Carlo simulations of the equilibrium autocorrelation times of the structure factor and of other large-scale density correlators for a particular value of the pullback $\alpha_{\rm crit}$. We explain this discrepancy. We then construct the continuum limit of the lifted TASEP, which remains integrable, and connect it to the event-chain Monte Carlo algorithm. The critical pullback $\alpha_{\rm crit}$ then equals the system pressure. We generalize the lifted TASEP to a large class of nearest-neighbor interactions, which lead to stationary states characterized by non-trivial Boltzmann distributions. By tuning the pullback parameter in the GL-TASEP to a particular value we can again achieve a polynomial speedup in the time required to converge to the steady state. We comment on the possible integrability of the GL-TASEP.