Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry

Abstract

Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological phase transition. However, the way of non-Hermiticity appearance may alter the system topology. By alternatively introducing the non-Hermiticity under symmetry to prevent nonzero imaginary magnetic flux, the bulk-boundary correspondence recovers and every bulk state becomes extended; the bulk topology of Bloch Hamiltonian predicts the (non)existence of edge states and topological phase transition. These are elucidated in a non-Hermitian Su-Schrieffer-Heeger model, where chiral-inversion symmetry ensures the vanishing of imaginary magnetic flux. The average value of Pauli matrices under the eigenstate of chiralinversion symmetric Bloch Hamiltonian defines a vector field, the vorticity of topological defects in the vector field is a topological invariant. Our findings are applicable in other non-Hermitian systems. We first uncover the roles played by non-Hermitian AB effect and chiral-inversion symmetry for the breakdown and recovery of bulk-boundary correspondence, and develop new insights for understanding non-Hermitian topological phases of matter. arXiv:1809.03139v3 [cond-mat.mes-hall]

Perspective on topological states of non-Hermitian lattices

“…Since the pioneering TKNN paper [2], this has been a crucial issue where progress is still underway even in Hermitian Hamiltonians [111,112]; the interested reader can find more extensive accounts on this topic in [8,10,113,114]. Different paths are currently being intensively explored in the quest for a bulkboundary correspondence that may allow for classification of the topological phases of non-Hermitian lattices [22,[115][116][117][118]. These forking paths arise because of the many possible options; the very first one is the use of the Hamiltonian or Green's functions as a starting point.…”

Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models

“…Similarly, the extension of the topological concepts developed for Hermitian quantum mechanics to these new systems has been a fruitful field of research 36 . Symmetry-based applications have been proposed [37][38][39][40] , but several notions are still actively discussed-the bulk-boundary correspondence being one 36,[41][42][43][44][45][46][47][48][49] . Indeed, the phase diagram of the same model can vary significantly depending on the choice of boundary conditions (open or periodic), a phenomenom dubbed the non-Hermitian skin effect.…”

Active topological photonics

“…It is also known that non-Hermiticity can explicitly disrupt the conventional bulk-boundary correspondence (BBC) held in Hermitian systems [119,130,[139][140][141][131][132][133][134][135][136][137][138]. Especially, asymmetric couplings make not only topological edge states but also non-topological bulk states localize around an either end to which the stronger hopping is directed (non-Hermitian skin effect) [ Fig.…”

“…Furthermore, imaginary gauge fields [135,[142][143][144], which indicate paired effective amplification in one way and attenuation to the other, are presented as an intelligible interpretation of these anomalous properties. The skin effect will hence stem from some symmetry breaking induced by non-Hermiticity [135,145]. General complex asymmetric (directional) couplings can break inversion symmetry and all the elemental symmetries (TRS ( †) and PRS ( †) ) for the AZ and AZ † classes.…”