Introduces a discrete formulation for the 3D winding number W3 based on θ-gaps, with unmodified and modified discrete fluxes that achieve quantization on fine grids.
Bundle gerbes for topological insulators
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abstract
Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter systems via equivariant bundle gerbes. The construction covers static and periodically driven systems with time reversal invariance in 2 and 3 space dimensions. It involves refinements of geometry of gerbes that are discussed in the first lecture, the second one being devoted to the applications to topological insulators.
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cond-mat.mes-hall 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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A discrete formulation for three-dimensional winding number
Introduces a discrete formulation for the 3D winding number W3 based on θ-gaps, with unmodified and modified discrete fluxes that achieve quantization on fine grids.