Toniolo, D;
(2022)
On the Bott index of unitary matrices on a finite torus.
Letters in Mathematical Physics
, 112
(6)
, Article 126. 10.1007/s11005-022-01602-6.
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Abstract
This article reviews the foundations of the theory of the Bott index of a pair of unitary matrices in the context of condensed matter theory, as developed by Hastings and Loring (J. Math. Phys. 51, 015214 (2010), Ann. Phys. 326, 1699 (2011), providing a novel proof of the equality with the Chern number. The Bott index is defined for a pair of unitary matrices, then extended to a pair of invertible matrices and homotopic invariance of the index is proven. An insulator defined on a lattice on a two-torus, that is a rectangular lattice with periodic boundary conditions, is considered and a pair of quasi-unitary matrices associated to this physical system are introduced. It is shown that their Bott index is well defined and the connection with the transverse conductance, the Chern number, is established proving the equality of the two quantities, in certain units.
| Type: | Article |
|---|---|
| Title: | On the Bott index of unitary matrices on a finite torus |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11005-022-01602-6 |
| Publisher version: | https://doi.org/10.1007/s11005-022-01602-6 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Bott index, Chern insulator, Homotopy invariance |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10162137 |
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