Dynamical phase behavior of the single and multilane asymmetric simple exclusion process via matrix product states
Abstract
The open asymmetric simple exclusion process (ASEP) has emerged as a paradigmatic model of nonequilibrium behavior, in part due to its complex dynamical behavior and wide physical applicability as a model of driven diffusion. We compare the dynamical phase behavior of the onedimensional (1D) ASEP and the multilane ASEP, a previously unstudied extension of the 1D model that may be thought of as a finitewidth strip of the fully twodimensional (2D) system. Our characterization employs large deviation theory (LDT), matrix product states (MPS), and the density matrix renormalization group (DMRG) algorithm, to compute the current cumulant generating function and its derivatives, which serve as dynamical order parameters. We use this measure to show that when particles cannot exit or enter the lattice vertically, the phase behavior of the multilane ASEP mimics that of its 1D counterpart, exhibiting the macroscopic and microscopic signatures of the maximal current, shock, and highdensitylowdensity coexistence phases. Conversely, when particles are allowed to freely enter and exit the lattice, no such transition is observed. This contrast emphasizes the complex interplay between latitudinal and longitudinal hopping rates and the effect of current biasing. Our results support the potential of tensor networks as a framework to understand classical nonequilibrium statistical mechanics.
 Publication:

Physical Review E
 Pub Date:
 August 2019
 DOI:
 10.1103/PhysRevE.100.022101
 arXiv:
 arXiv:1904.07336
 Bibcode:
 2019PhRvE.100b2101H
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 8 pages, 7 figures