Witnessing criticality in non-Hermitian systems via entopic uncertainty relation

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 propose an alternative proposal based on the entropy uncertainty relation (EUR) to detect the exceptional points and identify different phases of the non-Hermitian systems. We first investigate the EUR in a non-Hermitian system and then reveal a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitary Hermitian dynamics, the behaviors of EUR in the non-Hermitian system are well defined in two different ways depending on whether the system is located in unbroken or broken phase regimes. In unbroken phase regime where EUR undergoes an oscillatory behavior, while in broken phase regime where the oscillation of EUR breaks down. In the dynamical limit, we identify the critical phenomena of non-Hermitian systems in terms of the EUR. It is found that the EUR can exactly detect the critical points of non-Hermitian systems beyond PT-(anti-PT) symmetric systems. Finally, we comment on the possible experimental situation.