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Journal Article

The non-compact XXZ spin chain as stochastic particle process

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Frassek,  Rouven
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

arXiv:1904.02191.pdf
(Preprint), 529KB

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Citation

Frassek, R. (2019). The non-compact XXZ spin chain as stochastic particle process. Journal of Physics A, 52(33): 335202. doi:10.1088/1751-8121/ab2fb1.


Cite as: http://hdl.handle.net/21.11116/0000-0004-9B54-F
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.