Published 2020
| Accepted Version
Book Section - Chapter
Open
A class of two-dimensional AKLT models with a gap
Abstract
The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjectured that the two-dimensional version of their model on the hexagonal lattice exhibits a spectral gap. In this paper, we introduce a family of variants of the two-dimensional AKLT model depending on a positive integer n, which is defined by decorating the edges of the hexagonal lattice with one-dimensional AKLT spin chains of length n. We prove that these decorated models are gapped for all n ≥ 3.
Additional Information
© 2020 American Mathematical Society. This work arose from discussions during the follow-up workshop on Gapped Ground State Phases of Quantum Many-Body Systems to the 2018 Arizona School of Analysis and Mathematical Physics, organized by Robert Sims and two of the authors (H. A. and A. Y.) and supported by NSF Grant DMS-1800724. A. L. acknowledges support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY-1733907). B. N. acknowledges support by the National Science Foundation under Grant DMS-1813149 and a CRM-Simons Professorship for a stay at the Centre de Recherches Mathématiques (Montréal) during Fall 2018, where part of this work was carried out.Attached Files
Accepted Version - 1901.09297.pdf
Files
1901.09297.pdf
Files
(291.8 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:c7dba230a79a1c0b7c0f5d03d769d1ce
|
291.8 kB | Preview Download |
Additional details
- Eprint ID
- 105464
- Resolver ID
- CaltechAUTHORS:20200922-071519332
- DMS-1800724
- NSF
- Walter Burke Institute for Theoretical Physics, Caltech
- Sherman Fairchild Foundation
- Institute for Quantum Information and Matter (IQIM)
- PHY-1733907
- NSF
- DMS-1813149
- NSF
- Centre de Recherches Mathématiques (CRM)
- Created
-
2020-09-22Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
- Series Name
- Contemporary Mathematics
- Series Volume or Issue Number
- 741