A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains

Details A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains

2002-05-16

arxiv.org/abs/hep-th/0205169v1

J.Phys.A35:7187-7204,2002

Physics

High Energy Physics

High Energy Physics - Theory

19 pages Latex

Scientific paper

10.1088/0305-4470/35/33/314

We propose a dynamical matrix product ansatz describing the stochastic dynamics of two species of particles with excluded-volume interaction and the quantum mechanics of the associated quantum spin chains respectively. Analyzing consistency of the time-dependent algebra which is obtained from the action of the corresponding Markov generator, we obtain sufficient conditions on the hopping rates for identifing the integrable models. From the dynamical algebra we construct the quadratic algebra of Zamolodchikov type, associativity of which is a Yang Baxter equation. The Bethe ansatz equations for the spectra are obtained directly from the dynamical matrix product ansatz.

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