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Flow of unitary matrices: Real-space winding numbers in one and three dimensions

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arxiv 2405.12537 v2 pith:PEGUOV35 submitted 2024-05-21 nlin.CD cond-mat.mes-hall

F. Hamano , T. Fukui This is my paper · ORCID
classification nlin.CDcond-mat.mes-hall
keywords flowwindingdimensionsinvariancelatticenumbersystemsthree
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The notion of the flow introduced by Kitaev is a manifestly topological formulation of the winding number on a real lattice. First, we show in this paper that the flow is quite useful for practical numerical computations for systems without translational invariance. Second, we extend it to three dimensions. Namely, we derive a formula of the flow on a three-dimensional lattice, which corresponds to the conventional winding number when systems have translational invariance.

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  1. Winding number on 3D lattice

    hep-lat 2024-12 conditional novelty 6.0 of 10

    A tree-level improved lattice formula combined with an over-improved gradient flow reproduces integer winding numbers for T^3 to SU(2) maps on coarse lattices.

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