Spread complexity and localization in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="script">PT</mml:mi> </mml:math> -symmetric systems

Abstract

This study investigates the behavior of wave functions in parity-time (\ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}}) symmetric quantum systems, focusing on their spread and localization. Using a tight-binding chain model, the authors explore the dynamics under \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} symmetry and its breaking. By employing innovative quantum information measures, such as complexity, entropy, and inverse participation ratio in Krylov space, they quantify the wave function's distribution. In the \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}}-symmetric phase, the wave function spreads evenly, while \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} symmetry breaking leads to localization, exemplifying the non-Hermitian skin effect and edge modes.