Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics

Abstract

The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The properties of one- and two-dimensional representations are studied in detail and a general relation of the matrix algebra to that of the sequential limit is found. In this way the general phase diagram of the model is obtained. The mechanism of the sequential limit, the formulation as a vertex model and other aspects are discussed.

27 pages plain TeX, 5 figures included, PostScript for the complete paper at http://www.physik.fu-berlin.de/~ag-peschel/papers/mp.ps.gz, extra program at http://www.physik.fu-berlin.de/~ag-peschel/software/mp.html

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• On Matrix Product Ground States for Reaction-Diffusion Models
• Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
• The asymmetric exclusion model with sequential update
• Solution of a One-Dimensional Reaction-Diffusion Model with Spatial Asymmetry

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