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We analyze the dynamical phases of the current-biased 1D and multi-lane openasymmetric simple exclusion processes (ASEP), using matrix product states andthe density matrix renormalization group (DMRG) algorithm. In the 1D ASEP, wepresent a systematic numerical study of the current cumulant generatingfunction and its derivatives, which serve as dynamical phase order parameters.We further characterize the microscopic structure of the phases from localobservables and the entanglement spectrum. In the multi-lane ASEP, which may beviewed as finite width 2D strip, we use the same approach and find thelongitudinal current-biased dynamical phase behavior to be sensitive totransverse boundary conditions. Our results serve to illustrate the potentialof tensor networks in the simulation of classical nonequilibrium statisticalmodels.

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