A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains
arXiv:hep-th/0205169 · doi:10.1088/0305-4470/35/33/314
Abstract
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.
19 pages Latex
References in corpus (3)
Cited by in corpus (14)
- Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
- Exact solutions of exactly integrable quantum chains by a matrix product ansatz
- The Bethe ansatz as a matrix product ansatz
- Coupled Kardar-Parisi-Zhang Equations in One Dimension
- Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
- Determinant representation for some transition probabilities in the TASEP with second class particles
- Exactly solvable interacting vertex models
- Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
- Integrable Markov processes and quantum spin chains
- Transition probability and total crossing events in the multi-species asymmetric exclusion process
- Asymmetric exclusion model with impurities
- KPZ modes in -dimensional directed polymers
- Asymmetric exclusion model with several kinds of impurities
- Boundary-driven phase transitions in open two-species driven systems with an umbilic point