Witnessing criticality in non-Hermitian systems via entopic uncertainty relation

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 and accurate proposal based on the entropy uncertainty relation (EUR) to detect the exceptional points and identify different phases of the non-Hermitian systems. In particular, we 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 into two different ways depending on whether the system is located in unbroken or broken phase regimes. In the unbroken phase regime where EUR undergoes an oscillatory behavior, while in the broken phase regime where the oscillation of EUR breaks down. Moreover, we identify the critical phenomena of non-Hermitian systems in terms of the EUR in the dynamical limit. It is found that the EUR can detect exactly the critical points of non-Hermitian systems beyond (anti-)PT symmetric systems. Finally, we comment on the prospective experimental situation.