Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz

Abstract

We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct a parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named "fused" matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current.

33 pages, to appear in Nuclear Physics B

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• Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state
• Integrability of open boundary driven quantum circuits
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries
• Exact physical quantities of a competing spin chain in the thermodynamic limit
• Stroboscopic exclusion process: a first-moment-driven dynamics
• T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature