Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect

TL;DR

This paper establishes a unifying framework connecting quantum chaos and the non-Hermitian skin effect through space-time duality, revealing how boundary sensitivity relates to initial condition sensitivity in quantum systems.

Contribution

It introduces the concept of space-time duality to unify quantum chaos and non-Hermitian boundary effects, demonstrating their connection via out-of-time-ordered correlators in a specific model.

Findings

Out-of-time-ordered commutator maps to a two-point correlator in the dual non-Hermitian system

Sensitivity to initial conditions is linked to boundary effects through duality

Removing non-Hermiticity eliminates the sensitivity in the dual picture

Abstract

Quantum chaos in hermitian systems concerns the sensitivity of long-time dynamical evolution to initial conditions. The skin effect discovered recently in non-hermitian systems reveals the sensitivity to the spatial boundary condition even deeply in bulk. In this letter, we show that these two seemingly different phenomena can be unified through space-time duality. The intuition is that the space-time duality maps unitary dynamics to non-unitary dynamics and exchanges the temporal direction and spatial direction. Therefore, the space-time duality can establish the connection between the sensitivity to the initial condition in the temporal direction and the sensitivity to the boundary condition in the spatial direction. Here we demonstrate this connection by studying the space-time duality of the out-of-time-ordered commutator in a concrete chaotic hermitian model. We show that the out-of-time-ordered commutator is mapped to a special two-point correlator in a non-hermitian system in the dual picture. For comparison, we show that this sensitivity disappears when the non-hermiticity is removed in the dual picture.