Real-space representation of the second Chern number

2025/02/20 by Tsuyoshi Shiina, Shiina, T., F. Hamano +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Crystallography and Radiation Phenomena #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2502.14299

openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Kitaev's real-space formulation of the first Chern number to the second Chern number and establish a computational framework for its evaluation. To test its validity, we apply the derived formula to the disordered Wilson-Dirac model and analyze its ability to capture topological properties in the presence of disorder. Our results demonstrate that the real-space approach provides a viable method for characterizing higher-dimensional topological phases beyond momentum-space formulations.

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• Real-space second Chern number using the kernel polynomial method

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