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A discrete formulation for three-dimensional winding number (2403.05291v3)
Published 8 Mar 2024 in cond-mat.mes-hall, hep-lat, math-ph, and math.MP
Abstract: For a smooth map (g: X \to U(N)), where (X) is three-dimensional, oriented, and closed manifold, the winding number is defined as (W_3 = \frac{1}{24\pi2} \int_{X} \mathrm{Tr}\left[(g{-1}dg)3\right]). We introduce a method to compute (W_3) using a discrete approximation of (X) that manifestly ensures the quantization of (W_3).
- G. E. Volovik, The universe in a helium droplet, Vol. 117 (OUP Oxford, 2003).
- M. Lüscher, Topology of lattice gauge fields, Communications in Mathematical Physics 85, 39 (1982).
- T. Fujiwara, H. Suzuki, and K. Wu, Topological Charge of Lattice Abelian Gauge Theory, Progress of Theoretical Physics 105, 789 (2001), https://academic.oup.com/ptp/article-pdf/105/5/789/5186102/105-5-789.pdf .
- T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized brillouin zone: Efficient method of computing (spin) hall conductances, Journal of the Physical Society of Japan 74, 1674 (2005), https://doi.org/10.1143/JPSJ.74.1674 .
- F. Knöppel and U. Pinkall, Complex line bundles over simplicial complexes and their applications, in Advances in Discrete Differential Geometry, edited by A. I. Bobenko (Springer Berlin Heidelberg, Berlin, Heidelberg, 2016) pp. 197–239.
- K. Gaw\kedzki and N. Reis, WZW branes and gerbes, Reviews in Mathematical Physics 14, 1281 (2002), https://doi.org/10.1142/S0129055X02001557 .
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