Fragile PT-symmetry in a solvable model

TL;DR

This paper investigates a simple PT-symmetric quantum model, revealing that even tiny complex deformations can cause a sudden breakdown of the real spectrum, highlighting the fragile nature of PT-symmetry.

Contribution

It introduces an innovative approach to analyze PT-symmetric deformations in a solvable model, demonstrating the abrupt spectrum collapse caused by minimal complex perturbations.

Findings

Small complex deformations induce spectrum collapse

PT-symmetry is highly fragile in the model

Surprising sensitivity of the spectrum to perturbations

Abstract

One of the simplest pseudo-Hermitian models with real spectrum (viz., square-well on a real interval I of coordinates) is re-examined. A PT-symmetric complex deformation C of I is introduced and shown tractable via an innovated approach to matching conditions. The result is surprising: an arbitrarily small deformation I -> C implies a sudden collapse (i.e., the spontaneous PT-symmetry breaking) of virtually all the spectrum (i.e., up to its low-energy part).