Universität zu Köln

Alldridge, Alexander, Max, Christopher ORCID: 0000-0001-9887-0474 and Zirnbauer, Martin R. (2020). Bulk-Boundary Correspondence for Disordered Free-Fermion Topological Phases. Commun. Math. Phys., 377 (3). S. 1761 - 1822. NEW YORK: SPRINGER. ISSN 1432-0916

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Abstract

Guided by the many-particle quantum theory of interacting systems, we develop a uniform classification scheme for topological phases of disordered gapped free fermions, encompassing all symmetry classes of the TenfoldWay. We apply this scheme to give a mathematically rigorous proof of bulk-boundary correspondence. To that end, we construct real C*-algebras harbouring the bulk and boundary data of disordered free-fermion ground states. These we connect by a natural bulk-to-boundary short exact sequence, realising the bulk system as a quotient of the half-space theory modulo boundary contributions. To every ground state, we attach two classes in different pictures of real operator K-theory (or K R-theory): a bulk class, using Van Daele's picture, along with a boundary class, using Kasparov's Fredholm picture. We then show that the connecting map for the bulk-to-boundary sequence maps these K R-theory classes to each other. This implies bulk-boundary correspondence, in the presence of disorder, for both the strong and the weak invariants.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Alldridge, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Max, Christopher UNSPECIFIED orcid.org/0000-0001-9887-0474 UNSPECIFIED Zirnbauer, Martin R. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-130992
DOI:	10.1007/s00220-019-03581-7
Journal or Publication Title:	Commun. Math. Phys.
Volume:	377
Number:	3
Page Range:	S. 1761 - 1822
Date:	2020
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0916
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language K-THEORY; SYMMETRY CLASSES; HALL; DUALITY; EDGE; QUANTIZATION Multiple languages Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/13099