Homotopy characterization of non-Hermitian Hamiltonians

Wojcik, Charles C.; Sun, Xiao-Qi; Bzdušek, Tomáš; Fan, Shanhui

doi:10.1103/physrevb.101.205417

Homotopy characterization of non-Hermitian Hamiltonians

Journal Article · Fri May 15 00:00:00 EDT 2020 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.101.205417· OSTI ID:1803752

^[1]; Sun, Xiao-Qi ^[2]; Bzdušek, Tomáš ^[3]; Fan, Shanhui ^[2]

Stanford Univ., CA (United States); OSTI
Stanford Univ., CA (United States)
Stanford Univ., CA (United States); Paul Scherrer Inst. (PSI), Villigen (Switzerland); Univ. of Zurich (Switzerland)

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 $$\mathbb{Z}$$ winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups $$\mathbb{Z}_n$$ (rather than $$\mathbb{Z}$$ Chern number). Finally, 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOD; National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; Gordon and Betty Moore Foundation; Swiss National Science Foundation (SNF)

Grant/Contract Number:: SC0019380

OSTI ID:: 1803752

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 20 Vol. 101; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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