On Matrix Product Ground States for Reaction-Diffusion Models

TL;DR

This paper introduces a new algebraic approach to derive matrix product states for one-dimensional reaction-diffusion models, providing explicit representations and analyzing correlation functions at phase transitions.

Contribution

It presents a novel quadratic algebra involving four matrices for stationary states and explicitly constructs four-dimensional representations for a coagulation-decoagulation model.

Findings

Explicit four-dimensional matrix representations are obtained.

Exact expressions for physical quantities are derived.

The structure of n-point correlation functions at phase transition is characterized.

Abstract

We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a coagulation-decoagulation model explicit four-dimensional representations are given and exact expressions for various physical quantities are recovered. We also find the general structure of $n$-point correlation functions at the phase transition.