Spectral properties for a family of two-dimensional quantum antiferromagnets
Spectral properties for a family of two-dimensional quantum antiferromagnets
复制标题
二维量子反铁磁体族的光谱特性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Bartlett
中科院分区：
文献类型：
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作者：
Andrew S. Darmawan;S. Bartlett
我们研究二维 (2D) 晶格上的一系列量子反铁磁体的光谱特性。该模型系列是通过对 Affleck、Kennedy、Lieb 和 Tasaki (AKLT) 的经过充分研究的二维量子反铁磁模型进行变形而获得的；它们是由三色自旋格子上的二体、无挫折的哈密顿量来描述的。尽管 2D AKLT 模型中是否存在光谱间隙仍然是一个悬而未决的问题，但我们严格证明了该系列量子反铁磁体的子集存在光谱间隙。除了为二维 AKLT 型反铁磁体的能隙问题提供新进展外，这一结果还对量子计算理论产生了影响，因为它提供了一个二体哈密顿量族，其中基态是通用量子计算的资源，并且谱带隙被证明存在。
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.