The non-compact XXZ spin chain as stochastic particle process

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, 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 ##IMG##
[http://ej.iop.org/images/1751-8121/52/33/335202/aab2fb1ieqn001.gif] XXZ chain the associated
stochastic process reduces to the multiparticle asymmetric diffusion model introduced by
Sasamoto–Wadati.

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