Generally speaking, the energy spectra of non-Hermitian Hamiltonians are complex. However, for some specific systems, say those with parity-time symmetry, real-energy spectra could emerge and are separated to the domain of complex-energy spectra by exceptional points. The appearance of real-energy spectra (or exceptional points) may lead to distinguished quantum phenomena. This talk will discuss some new insights on non-Hermitian systems with real-energy spectra. Firstly, we give a general outline of how to construct Hermitian chiral boundary states out of topological insulators of non-Hermitian bulk states, even without parity-time symmetry. The transport of such Hermitian chiral boundary states significantly deviates from the paradigm of chiral boundary transport in Hermitian systems. Secondly, the level-repulsion problem near exceptional points is also considered.
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