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
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: | Article |
| Creators: | Creators Email ORCID ORCID Put Code Alldridge, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Zirnbauer, Martin R. UNSPECIFIED UNSPECIFIED UNSPECIFIED |
| URN: | urn:nbn:de:hbz:38-130992 |
| Identification Number: | 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 |
https://orcid.org/0000-0001-9887-0474Downloads
Downloads per month over past year
Altmetric
Export
Actions (login required)
 |
View Item |