Compact Wannier Functions in One Dimension Article Swipe

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YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2302.11608

Wannier functions have widespread utility in condensed matter physics and beyond. Topological physics, on the other hand, has largely involved the related notion of compactly-supported Wannier-type functions, which arise naturally in flat bands. In this paper, we establish a connection between these two notions, by finding the necessary and sufficient conditions under which compact Wannier functions exist in one dimension. We present an exhaustive construction of models with compact Wannier functions and show that the Wannier functions are unique, and in general, distinct from the corresponding maximally-localized Wannier functions.

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Wannier function Dimension (graph theory) Connection (principal bundle) Physics Pure mathematics Mathematics Quantum mechanics Theoretical physics Geometry

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2302.11608
PDF: https://arxiv.org/pdf/2302.11608
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4321853773

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DOI: https://doi.org/10.48550/arxiv.2302.11608

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Title: Compact Wannier Functions in One Dimension

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-02-22

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Authors: Pratik Sathe, Rahul Roy

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Landing page: https://arxiv.org/abs/2302.11608

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PDF URL: https://arxiv.org/pdf/2302.11608

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OA URL: https://arxiv.org/pdf/2302.11608

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Concepts: Wannier function, Dimension (graph theory), Connection (principal bundle), Physics, Pure mathematics, Mathematics, Quantum mechanics, Theoretical physics, Geometry

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Cited by: 0

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