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

Nicolas Crampé (1) , M. Evans , K. Mallick (2) , E. Ragoucy (3) , M. Vanicat (3)

1 L2C - Laboratoire Charles Coulomb
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

We present an explicit representation for the matrix product ansatz for sometwo-species TASEP with open boundary conditions. The construction relies on theintegrability of the models, a property that constrains the possible rates atthe boundaries. The realisation is built on a tensor product of copies of theDEHP algebras. Using this explicit construction, we are able to calculate thepartition function of the models. The densities and currents in the stationarystate are also computed. It leads to the phase diagram of the models. Dependingon the values of the boundary rates, we obtain for each species shock waves,maximal current, or low/high densities phases.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Nicolas Crampé, M. Evans, K. Mallick, E. Ragoucy, M. Vanicat. Matrix product solution to a 2-species TASEP with open integrable boundaries. Journal of Physics A: Mathematical and Theoretical, 2016, 49 (47), pp.475001. ⟨10.1088/1751-8113/49/47/475001⟩. ⟨hal-01341993⟩