Non-Hermitian topology of spontaneous magnon decay

McClarty, Paul A.; Rau, Jeffrey G.

doi:10.1103/physrevb.100.100405

Cited by 87 publications

(41 citation statements)

References 79 publications

(90 reference statements)

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“…Non-Hermitian Hamiltonians have widespread applications in describing open systems. For example, the ubiquitous loss and gain in photonic systems , the finite quasiparticle lifetimes [33][34][35][36][37], and certain statistical-mechanical models [38] are naturally described in terms of non-Hermitian Hamiltonians. Recently, there has been a growing interest in uncovering novel topological phases in non-Hermitian systems .…”

Section: Introductionmentioning

confidence: 99%

Homotopy characterization of non-Hermitian Hamiltonians

et al. 2020

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We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called "point-gap" and "line-gap" schemes. However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes. Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from Z winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups Z n (rather than Z Chern number). We interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.

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Section: Introductionmentioning

confidence: 99%

Homotopy characterization of non-Hermitian Hamiltonians

et al. 2020

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“…Recent theoretical studies have been focusing on topological systems in solid-state physics [70][71][72][73][74][75][76][77][78][79][80][81][82]. The bulk-edge correspondence has been notably under debate since it seems to be violated in contrast to Hermitian systems.…”

Section: Introductionmentioning

confidence: 99%

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Yokomizo

Murakami

2020

Phys. Rev. Research

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Energy bands of non-Hermitian crystalline systems are described in terms of the generalized Brillouin zone (GBZ) having unique features which are absent in Hermitian systems. In this paper, we show that in one-dimensional non-Hermitian systems with both sublattice symmetry and time-reversal symmetry such as the non-Hermitian Su-Schrieffer-Heeger model, a topological semimetal phase with exceptional points is stabilized by the unique features of the GBZ. Namely, under a change of a system parameter, the GBZ is deformed so that the system remains gapless. It is also shown that each energy band is divided into three regions, depending on the symmetry of the eigenstates, and the regions are separated by the cusps and the exceptional points in the GBZ.

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“…But there resides also a deeper conceptual issue: how is a Berry phase properly defined if there are no well-defined elementary particles because they hybridize with the continua of scattering states? The first steps are undertaken [58,75,167,168], but deeper insight is still missing. Strong magnon-magnon or triplon-triplon interactions can give rise to bound states.…”

Section: B Theoretical Challengesmentioning

confidence: 99%