Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics

TL;DR

This paper demonstrates that stationary states of a one-dimensional asymmetric exclusion process with parallel dynamics can be expressed using a matrix product formalism, enabling proof of conjectured correlation functions.

Contribution

It introduces a quadratic algebra with three matrices for the matrix product representation of the model's stationary states, advancing the analytical understanding of such processes.

Findings

Stationary states can be written in matrix product form.

The algebra involved is quadratic with three matrices.

Previous conjectures for correlation functions are proven.

Abstract

We show in the example of a one-dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form. The corresponding algebra is quadratic and involves three different matrices. Using this formalism we prove previous conjectures for the equal-time correlation functions of the model.