Construction of a matrix product stationary state from solutions of finite size system

Details Construction of a matrix product stationary state from solutions of finite size system Construction of a matrix product stationary state from solutions of finite size system

2004-03-09

arxiv.org/abs/cond-mat/0403235v2

J. Phys. A: Math. Gen. 37 (2004) 9873-9889

Physics

Condensed Matter

Statistical Mechanics

22 pages, no figure. Major changes: sec.3 was shortened; the list of references were changed. This is the final version, which

Scientific paper

10.1088/0305-4470/37/42/003

Stationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second, we give a method to construct the matrices from the stationary states of small size system when the above condition and $N\le M$ are satisfied. Third, the method by which one can check that the obtained matrices are valid for any system size is presented for the case where $M=N$ is satisfied. The application of our methods is explained using three examples: the asymmetric exclusion process, a model studied in [F. H. Jafarpour: J. Phys. A: Math. Gen. 36 (2003) 7497] and a hybrid of both of the models.

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