Topological insulators and \(C^{*}\)-algebras: theory and numerical practice

DOI10.1016/j.aop.2010.12.013zbMath1235.19003arXiv1012.1019OpenAlexW2079640725MaRDI QIDQ550602

Terry A. Loring, Matthew B. Hastings

Publication date: 13 July 2011

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1019

zbMATH Keywords

\(K\)-theorychiral symmetrytopological insulators\(C^{*}\)-algebra

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) General theory of (C^*)-algebras (46L05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Miscellaneous applications of (K)-theory (19M05)

Related Items (19)

Estimating bulk and edge topological indices in finite open chiral chains ⋮ A \(\mathbb{Z}_2\)-topological index for quasi-free fermions ⋮ Index pairings in presence of symmetries with applications to topological insulators ⋮ Topological insulators from the perspective of non-commutative geometry and index theory ⋮ Unnamed Item ⋮ Almost commuting unitary matrices related to time reversal ⋮ Computing a logarithm of a unitary matrix with general spectrum ⋮ Almost commuting orthogonal matrices ⋮ Almost commuting matrices, cohomology, and dimension ⋮ The noncommutative index theorem and the periodic table for disordered topological insulators and superconductors ⋮ Factorization of matrices of quaternions ⋮ The ℤ2 index of disordered topological insulators with time reversal symmetry ⋮ Wave-packet propagation in a finite topological insulator and the spectral localizer index ⋮ \(K\)-theory and pseudospectra for topological insulators ⋮ Pictures of \(KK\)-theory for real \(C^*\)-algebras and almost commuting matrices ⋮ Bulk spectrum and K-theory for infinite-area topological quasicrystals ⋮ Estimating Norms of Commutators ⋮ The spectral localizer for even index pairings ⋮ On the Bott index of unitary matrices on a finite torus

Uses Software

• mftoolbox

Cites Work

• Unnamed Item
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• Making almost commuting matrices commute
• Invariants of almost commuting unitaries
• Banach algebras and Bott periodicity
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• Almost commuting matrices, localized Wannier functions, and the quantum Hall effect
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• When matrices commute
• Topology and phases in fermionic systems
• Riemannian symmetric superspaces and their origin in random-matrix theory
• Functions of Matrices
• Lifting of nilpotent contractions
• Least squares, singular values and matrix approximations

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