Approximating the ground state of gapped quantum spin systems
Approximating the ground state of gapped quantum spin systems
复制标题
近似有隙量子自旋系统的基态
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Robert Sims
中科院分区：
文献类型：
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作者：
E. Hamza;S. Michalakis;B. Nachtergaele;Robert Sims
我们考虑定义在有限集合V上的量子自旋系统，该有限集合V具有度规。在典型的例子中，V是Zd的一个大的但有限的子集。对于有限范围的哈密顿量与一致有界的相互作用项和一个独特的，有间隙的基态，我们证明了相应的基态投影的局部性。在这样的系统中，这个基态投影仪可以近似的产品与可量化的支持可观。事实上，给定任何子集X ∈ V，基态投影可以近似为两个投影的乘积，一个支持在X上，另一个支持在Xc上，以及一个支持在边界区域上的有界可观测量，以这种方式，随着边界区域的增加，近似变得更好。这个结果推广到多维模型，黑斯廷斯的结果是他证明一维面积定律的重要组成部分[“一维量子系统的面积定律”，J. Stat.机械：理论实验2007，08024]。
We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Zd. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset X⊂V the ground state projector can be approximated by the product of two projections, one supported on X and one supported on Xc, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. This result generalizes to multidimensional models, a result of Hastings that was an important part of his proof of an area law in one dimension [“An area law for one dimensional quantum systems,” J. Stat. Mech.: Theory Exp. 2007, 08024].