2019/11/13 by Giuseppe De Nittis, Kyonori Gomi, Massimo Moscolari
Computer Science · Mathematics · Physics and Astronomy · #Abelian group #Differential geometry #Geometry #Mathematical physics #Mathematics #Pure mathematics #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena #cond-mat.mes-hall #math-ph #math.MP #msc:14D21. #msc:47B10 #msc:55N25 #msc:57R22
paper · pdf · doi:10.1016/j.geomphys.2020.103649
50 pages. Keywords: Landau Hamiltonian, non-Abelian magnetic field, "Real" and "Quaternionic" vector bundles, Dixmier trace
arxiv created 2019/11/13 · openalex publication_date 2020/03/19 · arxiv updated 2020/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The purpose of this paper is threefold: First of all the topological aspects of the Landau Hamiltonian are reviewed in the light (and with the jargon) of theory of topological insulators. In particular it is shown that the Landau Hamiltonian has a generalized even time-reversal symmetry (TRS). Secondly, a new tool for the computation of the topological numbers associated with each Landau level is introduced. The latter is obtained by combining the Dixmier trace and the (resolvent of the) harmonic oscillator. Finally, these results are extended to models with non-Abelian magnetic fields. Two models are investigated in details: the Jaynes-Cummings model and the "Quaternionic" model.