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Kennedy, R. and Zirnbauer, M. R. (2016). Bott Periodicity for Symmetric Ground States of Gapped Free-Fermion Systems. Commun. Math. Phys., 342 (3). S. 909 - 964. NEW YORK: SPRINGER. ISSN 1432-0916

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Abstract

Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a Bott clock topological classification of free-fermion ground states of gapped systems with symmetries. Our approach differs from previous ones in that (i) we work in the standard framework of Hermitian quantum mechanics over the complex numbers, (ii) we directly formulate a mathematical model for ground states rather than spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools rather than K-theory. Key to our proof is a natural transformation that squares to the standard Bott map and relates the ground state of a d-dimensional system in symmetry class s to the ground state of a (d + 1)-dimensional system in symmetry class s + 1. This relation gives a new vantage point on topological insulators and superconductors.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kennedy, R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Zirnbauer, M. R. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-283219
DOI:	10.1007/s00220-015-2512-8
Journal or Publication Title:	Commun. Math. Phys.
Volume:	342
Number:	3
Page Range:	S. 909 - 964
Date:	2016
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0916
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TOPOLOGICAL QUANTUM-SYSTEMS; BUNDLES; CLASSIFICATION Multiple languages Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28321