Existence and stability of PTPT-symmetric states in nonlinear two-dimensional square lattices

• We present a study on stationary states in PT-symmetric lattice settings in the weak coupling limit.
• We report the existence and stability properties of PT-symmetric soliton and vortex configurations.
• All examined vortex configurations are unstable with respect to small perturbations.
• One branch of solutions extending soliton configurations is spectrally stable.
• This offers an analytical perspective to this topic and corroborates results by numerical results.

Solitons and vortices symmetric with respect to simultaneous parity (PP) and time reversing (TT) transformations are considered on the square lattice in the framework of the discrete nonlinear Schrödinger equation. The existence and stability of such PTPT-symmetric configurations is analyzed in the limit of weak coupling between the lattice sites, when predictions on the elementary cell of a square lattice (i.e., a single square) can be extended to a large (yet finite) array of lattice cells. In particular, we find all examined vortex configurations are unstable with respect to small perturbations while a branch extending soliton configurations is spectrally stable. Our analytical predictions are found to be in good agreement with numerical computations.