Bulk–Boundary Correspondence for Sturmian Kohmoto-Like Models View Full Text


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Article Info

DATE

2019-03-27

AUTHORS

Johannes Kellendonk, Emil Prodan

ABSTRACT

We consider one-dimensional tight binding models on ℓ2(Z) whose spatial structure is encoded by a Sturmian sequence (ξn)n∈{a,b}Z. An example is the Kohmoto Hamiltonian, which is given by the discrete Laplacian plus an on-site potential vn taking value 0 or 1 according to whether ξn is a or b. The only non-trivial topological invariants of such a model are its gap labels. The bulk–boundary correspondence we establish here states that there is a correspondence between the gap label and a winding number associated with the edge states, which arises if the system is augmented and compressed onto half-space ℓ2(N). This has been experimentally observed with polaritonic waveguides. A correct theoretic explanation requires, however, first a smoothing out of the atomic motion via phason flips. With such an interpretation at hand, the winding number corresponds to the mechanical work through a cycle which the atomic motion exhibits on the edge states. More... »

PAGES

1-32

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  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s00023-019-00792-5

    DOI

    http://dx.doi.org/10.1007/s00023-019-00792-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1113043324


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