Origin of maximal symmetry breaking in even PT-symmetric lattices

TL;DR

This paper investigates the origin of maximal PT-symmetry breaking in even PT-symmetric lattices with impurities, deriving an exact relation for the critical impurity strength and showing its dependence on the lattice profile.

Contribution

The paper provides an exact derivation linking the critical impurity strength to the hopping amplitude between impurities in PT-symmetric lattices.

Findings

Critical impurity strength equals the hopping amplitude between impurities.

Maximal PT-symmetry breaking involves the emergence of complex eigenvalues.

Threshold strength can be tuned by changing the lattice profile.

Abstract

By investigating a parity and time-reversal (PT) symmetric, $N$-site lattice with impurities $\pm i\gamma$ and hopping amplitudes $t_0 (t_b)$ for regions outside (between) the impurity locations, we probe the origin of maximal PT-symmetry breaking that occurs when the impurities are nearest neighbors. Through a simple and exact derivation, we prove that the critical impurity strength is equal to the hopping amplitude between the impurities, $\gamma_c=t_b$, and the simultaneous emergence of $N$ complex eigenvalues is a robust feature of any PT-symmetric hopping profile. Our results show that the threshold strength $\gamma_c$ can be widely tuned by a small change in the global profile of the lattice, and thus have experimental implications.