T-duality simplifies bulk-boundary correspondence

Abstract

Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that T-duality trivializes the bulk-boundary correspondence.

29 pages, title changed, minor changes, and new references added. To appear in CMP

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Cited by in corpus (19)

• The $K$-theoretic bulk-edge correspondence for topological insulators
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• Differential topology of semimetals
• Bulk-boundary correspondence for disordered free-fermion topological phases
• Global topology of Weyl semimetals and Fermi arcs
• Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces
• T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
• Fu-Kane-Mele monopoles in semimetals
• T-duality simplifies bulk-boundary correspondence: the noncommutative case
• Bulk-edge correspondence and the cobordism invariance of the index
• The non-commutative topology of two-dimensional dirty superconductors
• Gap-labelling conjecture with nonzero magnetic field
• Twisted crystallograpic T-duality via the Baum--Connes isomorphism
• T-duality and the bulk-boundary correspondence
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Classification of topological invariants related to corner states
• Classifying bulk-edge anomalies in the Dirac Hamiltonian
• Geometric foundations for classical $\mathrm{U}(1)$-gauge theory on noncommutative manifolds
• Engineering of Anyons on M5-Probes via Flux Quantization