The Haldane model and its localization dichotomy

zbMath1414.81122arXiv1909.03298MaRDI QIDQ5378102

Massimo Moscolari, Domenico Monaco, Gianluca Panati, Giovanna Marcelli

Publication date: 11 June 2019

Full work available at URL: https://arxiv.org/abs/1909.03298

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Many-body theory; quantum Hall effect (81V70) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (10)

From charge to spin: Analogies and differences in quantum transport coefficients ⋮ Beyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau Hamiltonians ⋮ Mathematical aspects of the Kubo formula for electrical conductivity with dissipation ⋮ Unified Approach to Floquet Lattices, Topological Insulators, and Their Nonlinear Dynamics ⋮ Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators ⋮ Středa formula for charge and spin currents ⋮ Localised module frames and Wannier bases from groupoid Morita equivalences ⋮ Symmetry and localization for magnetic Schrödinger operators: Landau levels, Gabor frames and all that ⋮ Purely linear response of the quantum Hall current to space-adiabatic perturbations ⋮ Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher

Cites Work

• Unnamed Item
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• Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions
• Universality of the Hall conductivity in interacting electron systems
• The existence of generalised Wannier functions for one-dimensional systems
• Optimal decay of Wannier functions in Chern and quantum Hall insulators
• Topology of Sobolev mappings. II.
• Symmetry and localization for magnetic Schrödinger operators: Landau levels, Gabor frames and all that
• Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry
• Triviality of Bloch and Bloch-Dirac bundles
• Topological invariants of eigenvalue intersections and decrease of Wannier functions in graphene
• An overview of periodic elliptic operators

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