Abstract
We investigate the parity- and time-reversal (-) symmetry breaking in lattice models in the presence of long-ranged, non-Hermitian, -symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile threshold for an open finite lattice, we show that continuum loss-gain potentials have a positive -breaking threshold for , and a zero threshold for . When localized states with complex (conjugate) energies in the continuum energy band occur at higher loss-gain strengths. We investigate the signatures of -symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time scale in the -symmetry broken region.
- Received 17 March 2014
- Revised 7 July 2014
DOI:https://doi.org/10.1103/PhysRevA.90.032108
©2014 American Physical Society