Exact matrix-product states for parallel dynamics: open boundaries and excess mass on thering

Abstract

In this paper it is shown that the steady state weights of the asymmetric simple exclusionprocess (ASEP) with open boundaries and parallel update can be written as a product of ascalar pair-factorized and a matrix-product state. This type of state is also obtained foran ASEP on a ring in which particles can move one or two sites. The dynamicsleads to the formation of an excess hole that plays the role of a defect. In thecontinuous-time limit the process recovers the ASEP with a single defect particle.The phase diagram shows a first-order phase transition between two phases withdifferent defect velocities. These are calculated exactly from the process-generatingfunction.