Blackett Laboratory, Imperial College London, London, United Kingdom
摘要: Systems which exhibit gain/loss can often be described by effective Hamiltonians which are non-Hermitian. In this talk, I will review recent advances in our understanding of symmetry-protected topological phase transitions in the absence of Hermiticity. As a starting point, I shall describe results concerning non-Hermitian generalizations of the paradigmatic Su-Schrieffer-Heeger (SSH) model. This minimal model has shed light on several unique features that have no conventional counterparts. These include: gapless spectra away from topological transition points, new symmetries responsible for edge mode stability, invariants related to exceptional points, and anomalous bulk-boundary correspondence. Various flavors of "pseudo-Hermiticity" appear important in protecting the topological phases. I suggest a symmetry classification which may form the basis towards a generalization of the standard "ten-fold way". This presentation aims to provide an overview of recent results, as well as an outlook for future research directions in this rapidly-growing field.