Quantum entanglement of non-Hermitian quasicrystals

As a hallmark of a pure quantum effect, quantum entanglement has provided unconventional routes to characterize condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian quasicrystals. We study a class of experimentally realizable models for non-Hermitian quasicrystal chains, in which asymmetric hopping and complex potential coexist. We diagnose the global phase diagram by means of entanglement from both the real-space and momentum-space partitions. By measuring the entanglement entropy, we numerically determine the metal-insulator transition point. We com-bine real-space and momentum-space entanglement spectra to complementarily characterize the delocalization phase and the localization phase. Inspired by the entanglement spectrum, we further analytically prove that a duality exists between the two phase regions. The transition point is self-dual and exact, further validating the numerical result from diagonalizing non-Hermitian matrices. Finally, we identify the mobility edge by means of entanglement.