  The asymmetric simple exclusion process (ASEP) is a paradigmatic
driven-diffusive system that describes the asymmetric diffusion of particles
with hardcore interactions in a lattice. Although the ASEP is known as an
exactly solvable model, most exact results are limited to one-dimensional
systems. Recently, the exact steady state in the multi-dimensional ASEP has
been proposed [1]. The research focused on the situation where the number of
particles is conserved. In this paper, we consider the two-dimensional ASEP
with the attachment and detachment of particles (ASEP-LK), where particle
number conservation is violated. By employing the result in Ref. [1], we
construct the exact steady state of the ASEP-LK and reveal its properties
through the exact computation of physical quantities.
