Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

TL;DR

This paper explores how entropic uncertainty relations can serve as indicators of critical points and phase transitions in non-Hermitian systems, especially around exceptional points, revealing different behaviors in unbroken and broken phases.

Contribution

It establishes a novel connection between entropic uncertainty relations and exceptional points in non-Hermitian systems, providing a new method to detect phase transitions.

Findings

EUR oscillates in unbroken phase

EUR breaks down in broken phase

Exceptional points mark transition between behaviors

Abstract

Non-Hermitian systems with exceptional points lead to many intriguing phenomena due to the coalescence of both eigenvalues and corresponding eigenvectors, in comparison to Hermitian systems where only eigenvalues degenerate. In this paper, we have investigated entropic uncertainty relation (EUR) in a non-Hermitian system and revealed a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitarity dynamics determined by a Hermitian Hamiltonian, the behaviors of EUR can be well defined in two different ways depending on whether the system is located in unbroken phase or broken phase regimes. In unbroken phase regime, EUR undergoes an oscillatory behavior while in broken phase regime where the oscillation of EUR breaks down. The exceptional points mark the oscillatory and non-oscillatory behaviors of the EUR. In the dynamical limit, we have identified the witness of critical behavior of non-Hermitian systems in terms of the EUR. Our results reveal that the witness can detect exactly the critical points of non-Hermitian systems beyond (anti-) PT-symmetric systems. Our results may have potential applications to witness and detect phase transition in non-Hermitian systems.