Causality and phase transitions in PT-symmetrical optical systems
  We discuss phase transitions in PT-symmetric optical systems. We show that due to frequency dispersion of the dielectric permittivity, an optical system can have PT-symmetry at isolated frequency points only. An assumption of the existence of a PT-symmetric system in a continuous frequency interval violates the causality principle. Therefore, the ideal symmetry-breaking transition cannot be observed by simply varying the frequency. 
A. A. Zyablovsky, A. P. Vinogradov, A. V. Dorofeenko, A. A. Pukhov,   and A. A. Lisyansky
physics.optics cond-mat.mes-hall quant-ph