Partially asymmetric exclusion process with open boundaries

Exclusive diffusion on a one-dimensional lattice is studied. In the model, particles hop stochastically in both directions but with different rates. At the ends of the lattice, particles are injected and removed. The exact stationary probability measure is represented in the form of a matrix product, as a generalization of the solution given by Derrida et al. [J. Phys. A 26, 1493 (1993)] for the fully asymmetric process. The phase diagram of the current on the infinite lattice is obtained. Analytic expressions for the current in the different phases are derived. The model is equivalent to an XXZ-Heisenberg chain with a certain type of boundary terms, the ground state of which corresponds to the stationary solution of the master equation.