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

Autor:	Vanicat, Matthieu
Rok vydání:	2017
Předmět:	Mathematical Physics Condensed Matter - Statistical Mechanics Condensed Matter - Strongly Correlated Electrons Nonlinear Sciences - Cellular Automata and Lattice Gases Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1016/j.nuclphysb.2018.02.007
Popis:	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. Comment: 33 pages, to appear in Nuclear Physics B
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1711.08884 Zobrazit plný text záznamu View this record from Arxiv