Towards a Matrix Product Ansatz in Two Dimensions (opens in new tab)

Matrix product ansatz (MPA) is a powerful framework for constructing exact steady state weights of one dimensional non-equilibrium stochastic processes; but its generalization to higher dimensions is limited. Here, we introduce the MPA formalism for two dimensions (2D). As a concrete application, we introduce and exactly solve a non-conserved assisted exclusion model (NAEM) in one and two dimensions with constrained hopping and local birth-death...