The non-compact XXZ spin chain as stochastic particle process

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.

arXiv comment15 pages, 1 figure

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Cited by in corpus (6)

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• Non-compact quantum spin chains as integrable stochastic particle processes
• Exact solution of an integrable non-equilibrium particle system
• Integrable boundaries for the q-Hahn process
• The steady state of the boundary-driven multiparticle asymmetric diffusion model
• BC-type open $SL(2,\mathbb{C})$ spin chain