Spectral properties for a family of two-dimensional quantum antiferromagnets
Abstract
We study the spectral properties of a family of quantum antiferromagnets on two-dimensional (2D) lattices. This family of models is obtained by a deformation of the well-studied 2D quantum antiferromagnetic model of Affleck, Kennedy, Lieb and Tasaki (AKLT); they are described by two-body, frustration-free Hamiltonians on a three-colourable lattice of spins. Although the existence of a spectral gap in the 2D AKLT model remains an open question, we rigorously prove the existence of a gap for a subset of this family of quantum antiferromagnets. Along with providing new progress for the gap problem in AKLT-type antiferromagnets in 2D, this result has implications for the theory of quantum computation as it provides a family of two-body Hamiltonians for which the ground state is a resource for universal quantum computation and for which a spectral gap is proven to exist.
Keywords
Cite
@article{arxiv.1509.04719,
title = {Spectral properties for a family of two-dimensional quantum antiferromagnets},
author = {Andrew S. Darmawan and Stephen D. Bartlett},
journal= {arXiv preprint arXiv:1509.04719},
year = {2016}
}
Comments
14 pages, 6 figures, comments welcome; v2 published version