Bott periodicity for \(\mathbb Z_2\) symmetric ground states of gapped free-fermion systems

DOI10.1007/s00220-015-2512-8zbMath1346.81159arXiv1409.2537OpenAlexW3102084054WikidataQ59470327 ScholiaQ59470327MaRDI QIDQ261623

F. Blanchet-Sadri, M. Dambrine

Publication date: 24 March 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.2537

zbMATH Keywords

Bott periodicitygapped free-fermion systemssymmetric ground states

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Topological properties in algebraic geometry (14F45)

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Cites Work

• Unnamed Item
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• On the \(K\)-theoretic classification of topological phases of matter
• Twisted equivariant matter
• Classification of ``real Bloch-bundles: topological quantum systems of type AI
• Transformation groups
• Classification of ``quaternionic Bloch-bundles: topological quantum systems of type AII
• The stable homotopy of the classical groups
• Clifford modules
• Symmetry classes of disordered fermions
• CLIFFORD MODULES AND SYMMETRIES OF TOPOLOGICAL INSULATORS
• Symmetries, dimensions and topological insulators: the mechanism behind the face of the Bott clock
• Periodic table for topological insulators and superconductors
• Morse Theory. (AM-51)
• K-THEORY AND REALITY
• Symplectic Bundles and $KR$-Theory.