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A class of two-dimensional AKLT models with a gap

Abdul-Rahman, Houssam
•
Lemm, Marius  
•
Lucia, Angelo
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2020
Contemporary Mathematics

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 integern, which is defined by decorating the edges of the hexagonal lattice with one-dimensional AKLT spin chains of lengthn. We prove that these decorated models are gapped for alln≥3.

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Type
book part or chapter
DOI
10.1090/conm/741/14917
Author(s)
Abdul-Rahman, Houssam
Lemm, Marius  
Lucia, Angelo
Nachtergaele, Bruno
Young, Amanda
Date Issued

2020

Publisher

American Mathematical Society

Publisher place

Providence, Rhode Island

Published in
Contemporary Mathematics
ISBN of the book

978-1-4704-4841-7

Start page

1

End page

21

URL
http://www.ams.org/conm/741
Written at

OTHER

EPFL units
CAMP  
Available on Infoscience
October 1, 2020
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/172108
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