Non-compact Quantum Spin Chains as Integrable Stochastic Particle Processes

@article{Frassek2019NoncompactQS,
  title={Non-compact Quantum Spin Chains as Integrable Stochastic Particle Processes},
  author={Rouven Frassek and Cristian Giardin{\`a} and Jorge Kurchan},
  journal={Journal of Statistical Physics},
  year={2019}
}
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and [Povolotsky] in the context of KPZ universality class. We show that they may be mapped onto an integrable $\mathfrak{sl}(2)$ Heisenberg spin chain whose Hamiltonian density in the bulk has been already studied in the AdS/CFT and the integrable system literature. Using the quantum inverse scattering method, we… 
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