The Geometry of (non-Abelian) Landau levels

Abstract

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.

arXiv comment50 pages. Keywords: Landau Hamiltonian, non-Abelian magnetic field, "Real" and "Quaternionic" vector bundles, Dixmier trace

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Cited by in corpus (7)

• Cobordism invariance of topological edge-following states
• Bulk-edge correspondence for unbounded Dirac-Landau operators
• The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects
• From orbital magnetism to bulk-edge correspondence
• Dixmier trace and the DOS of magnetic operators
• The noncommutative geometry of the Landau Hamiltonian: Differential aspects
• Ultra-generalized Wannier bases: Are they relevant to topological transport?