An investigation of PT -symmetry breaking in tight-binding chains

Abstract

AbstractWe consider non-HermitianPT-symmetric tight-binding chains where gain/loss optical potentials of equal magnitudes ±iγare arbitrarily distributed over all sites. The main focus is on the thresholdγcbeyond whichPT-symmetry is broken. This threshold generically falls off as a power of the chain length, whose exponent depends on the configuration of optical potentials, ranging between 1 (for balanced periodic chains) and 2 (for unbalanced periodic chains, where each half of the chain experiences a non-zero mean potential). For random sequences of optical potentials with zero average and finite variance, the threshold is itself a random variable, whose mean value decays with exponent 3/2 and whose fluctuations have a universal distribution. The chains yielding the most robustPT-symmetric phase, i.e. the highest threshold at fixed chain length, are obtained by exact enumeration up to 48 sites. This optimal threshold exhibits an irregular dependence on the chain length, presumably decaying asymptotically with exponent 1, up to logarithmic corrections.