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Topological Quantum Computing
Topological Classification of Insulators: II. Quasi-Two-Dimensional Locality
arXiv
Authors: Jui-Hui Chung, Jacob Shapiro
Year
2024
Paper ID
66775
Status
Preprint
Abstract Read
~2 min
Abstract Words
93
Citations
N/A
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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- This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
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- We provide an alternative characterization of two-dimensional locality (necessary e.g.
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