Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics

TL;DR

This paper develops a matrix product state approach to analyze the stationary states of a one-dimensional lattice gas with parallel dynamics, revealing phase diagrams and algebraic structures.

Contribution

It introduces a novel matrix product state formulation for parallel dynamics in lattice gases, connecting algebraic structures to phase behavior.

Findings

Stationary states expressed as alternating matrix products.

Detailed analysis of one- and two-dimensional representations.

Established relation between matrix algebra and sequential limit.

Abstract

The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The properties of one- and two-dimensional representations are studied in detail and a general relation of the matrix algebra to that of the sequential limit is found. In this way the general phase diagram of the model is obtained. The mechanism of the sequential limit, the formulation as a vertex model and other aspects are discussed.