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arXiv · 2406.05385

Topological Classification of Insulators: II. Quasi-Two-Dimensional Locality

Jui-Hui Chung·Jacob Shapiro
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Abstract

We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this abstract characterization, we define generalizations of this locality, which we term quasi-2D. We go on to calculate the path-connected components of spaces of unitaries or orthogonal projections which are quasi-2D-local and find a starkly different behavior compared with the actual 2D column of the Kitaev table, exhibiting e.g., in the unitary chiral case, infinitely many $\mathbb{Z}$-valued indices.

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Jui-Hui Chung, Jacob Shapiro. 2024-06-08. Topological Classification of Insulators: II. Quasi-Two-Dimensional Locality. https://arxiv.org/abs/2406.05385

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