Multispecies TASEP and the tetrahedron equation. (2nd February 2016)

• Record Type: Journal Article
• Authors: Kuniba, Atsuo; Maruyama, Shouya; Okado, Masato
• Is Part Of: Journal of physics. Volume 49:Number 11(2016)
• Publication Date: 2016-02-02
• Subjects: multispecies TASEP -- tetrahedron equation -- layer to layer transfer matrix; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/11/114001
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We introduce a family of layer to layer transfer matrices in a three-dimensional (3D) lattice model which can be viewed as partition functions of the q -oscillator valued six-vertex model on an m × n square lattice. By invoking the tetrahedron equation we establish their commutativity and bilinear relations mixing various boundary conditions. At q = 0 and m = n, they ultimately yield a new proof of the steady state formula for the n -species totally asymmetric simple exclusion process obtained recently by the authors, revealing the 3D integrability in the matrix product construction.