# The non-compact XXZ spin chain as stochastic particle process

## TL;DR

This paper establishes a connection between the non-compact XXZ spin chain Hamiltonian and a stochastic particle process, revealing new insights into multi-particle dynamics and extending known models like ASEP.

## Contribution

It introduces a novel relation between the non-compact XXZ spin chain and a q-Hahn zero range process, highlighting differences from traditional exclusion processes.

## Key findings

- Identifies the hopping rates with a q-Hahn asymmetric zero range model.
- Shows the process reduces to the Sasamoto-Wadati multiparticle diffusion model for spin 1/2.
- Extends the understanding of stochastic processes related to integrable quantum spin chains.

## Abstract

In this note we relate the Hamiltonian of the integrable non-compact spin $s$ XXZ chain to the Markov generator of a stochastic particle process. The hopping rates of the continuous-time process are identified with the ones of a q-Hahn asymmetric zero range model. The main difference with the asymmetric simple exclusion process (ASEP), which can be mapped to the ordinary XXZ spin chain, is that multiple particles can occupy one and the same site. For the non-compact spin $\frac{1}{2}$ XXZ chain the associated stochastic process reduces to the multiparticle asymmetric diffusion model introduced by Sasamoto-Wadati.