Dynamic Screening in a Two-Species Asymmetric Exclusion Process

TL;DR

This paper investigates a two-species driven lattice gas model, demonstrating that its dynamic scaling behavior aligns with KPZ universality due to perfect fluctuation screening, and introduces a topological invariant in the stationary state.

Contribution

It provides a rigorous proof of fluctuation screening in a two-species exclusion process and shows the process remains in the KPZ universality class with a factorized structure.

Findings

Dynamic critical exponent consistent with KPZ scaling

Exponential decay of two-point correlations due to screening

Existence of a topological invariant in the stationary state

Abstract

The dynamic scaling properties of the one dimensional Burgers equation are expected to change with the inclusion of additional conserved degrees of freedom. We study this by means of 1-D driven lattice gas models that conserve both mass and momentum. The most elementary version of this is the Arndt-Heinzel-Rittenberg (AHR) process, which is usually presented as a two species diffusion process, with particles of opposite charge hopping in opposite directions and with a variable passing probability. From the hydrodynamics perspective this can be viewed as two coupled Burgers equations, with the number of positive and negative momentum quanta individually conserved. We determine the dynamic scaling dimension of the AHR process from the time evolution of the two-point correlation functions, and find numerically that the dynamic critical exponent is consistent with simple Kardar-Parisi-Zhang (KPZ) type scaling. We establish that this is the result of perfect screening of fluctuations in the stationary state. The two-point correlations decay exponentially in our simulations and in such a manner that in terms of quasi-particles, fluctuations fully screen each other at coarse grained length scales. We prove this screening rigorously using the analytic matrix product structure of the stationary state. The proof suggests the existence of a topological invariant. The process remains in the KPZ universality class but only in the sense of a factorization, as $({KPZ})^2$. The two Burgers equations decouple at large length scales due to the perfect screening.