Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states

We analyze the dynamical phases of the current-biased 1D and multi-lane open asymmetric simple exclusion processes (ASEP), using matrix product states and the density matrix renormalization group (DMRG) algorithm. In the 1D ASEP, we present a systematic numerical study of the current cumulant generating function and its derivatives, which serve as dynamical phase order parameters. We further characterize the microscopic structure of the phases from local observables and the entanglement spectrum. In the multi-lane ASEP, which may be viewed as finite width 2D strip, we use the same approach and find the longitudinal current-biased dynamical phase behavior to be sensitive to transverse boundary conditions. Our results serve to illustrate the potential of tensor networks in the simulation of classical nonequilibrium statistical models.