A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains

TL;DR

This paper introduces a dynamical matrix product ansatz to identify integrable models in stochastic particle dynamics and quantum spin chains, linking algebraic structures to solvability conditions.

Contribution

It provides a new criterion for integrability based on algebraic consistency, connecting stochastic dynamics with quantum integrable systems via the Yang-Baxter equation.

Findings

Derived sufficient conditions on hopping rates for integrability.

Constructed the quadratic algebra of Zamolodchikov type.

Obtained Bethe ansatz equations directly from the ansatz.

Abstract

We propose a dynamical matrix product ansatz describing the stochastic dynamics of two species of particles with excluded-volume interaction and the quantum mechanics of the associated quantum spin chains respectively. Analyzing consistency of the time-dependent algebra which is obtained from the action of the corresponding Markov generator, we obtain sufficient conditions on the hopping rates for identifing the integrable models. From the dynamical algebra we construct the quadratic algebra of Zamolodchikov type, associativity of which is a Yang Baxter equation. The Bethe ansatz equations for the spectra are obtained directly from the dynamical matrix product ansatz.