Stochastic higher spin vertex models on the line

TL;DR

This paper introduces a new family of exactly solvable stochastic particle systems on the line, unifying and extending models like ASEP and q-TASEP through Bethe ansatz and R-matrix fusion techniques.

Contribution

It develops a four-parameter family of models that can be explicitly diagonalized and connected to many known and new integrable systems within the KPZ universality class.

Findings

Explicit Bethe ansatz eigenfunctions derived.

Contour integral and Fredholm determinant formulas established.

Models include ASEP, stochastic six-vertex, q-TASEP, and directed polymers.

Abstract

We introduce a four-parameter family of interacting particle systems on the line which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain Markov dualities. Using this, for the systems started in step initial data we write down nested contour integral formulas for moments and Fredholm determinant formulas for Laplace-type transforms. Taking various choices or limits of parameters, this family degenerates to many of the known exactly solvable models in the Kardar-Parisi-Zhang universality class, as well as leads to many new examples of such models. In particular, ASEP, the stochastic six-vertex model, q-TASEP and various directed polymer models all arise in this manner. Our systems are constructed from stochastic versions of the R-matrix related to the six-vertex model. One of the key tools used here is the fusion of R-matrices and we provide a probabilistic proof of this procedure.