Matrix product solution to a 2-species TASEP with open integrable boundaries

We present an explicit representation for the matrix product ansatz for some two-species totally asymmetric exclusion process with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries. The realisation is...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2016-10, Vol.49 (47), p.475001
Main Authors: Crampe, N, Evans, M R, Mallick, K, Ragoucy, E, Vanicat, M
Format: Article
Language:English
Subjects:
algebraic Bethe ansatz
Condensed Matter
exclusion process
integrable systems
matrix ansatz
nonequilibrium statistical mechanics
open boundaries
Physics
Statistical Mechanics
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Summary:We present an explicit representation for the matrix product ansatz for some two-species totally asymmetric exclusion process with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries. The realisation is built on a tensor product of copies of the DEHP algebras. Using this explicit construction, we are able to calculate the partition function of the models. The densities and currents in the stationary state are also computed and led to the phase diagrams of the models. Depending on the values of the boundary rates, we obtain for each species shock waves, maximal current, or low/high densities phases.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/49/47/475001