Quantum Entanglement of Non-Hermitian Quasicrystals

Abstract: As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian quasicrystals. We present a class of experimentally realizable models for non-Hermitian quasicrystal chains, in which asymmetric hopping and complex potential coexist. We diagnose global phase diagram by means of entanglement from both real-space and momentum-space partition. By measuring entanglement entropy, we numerically determine the metal-insulator transition point. We combine real-space and momentum-space entanglement spectra to complementarily characterize the delocalization phase and the localization phase. Inspired by 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 mobility edge by means of entanglement.