无阻挫系统中关联长度与间隙的关系
Correlation Length versus Gap in Frustration-Free Systems
摘要：
黑斯廷斯建立了带隙量子多体系统的基态的关联指数衰减。具有谱隙$ε$的（几何上）局部哈密顿量的基态具有上界为$ξ=O(1/ε)$的相关长度$ξ$。一般来说，这个界限是无法改善的。在这里，我们研究的相关长度作为一个函数的频谱间隙的挫折免费本地哈密顿的缩放，我们证明了一个紧束缚$ξ=O(1/\sqrtε)$在这种设置。这突出了无挫折和接近临界的挫折系统之间的根本区别。结果是使用阿哈罗诺夫，阿拉德，Vazirani和Landau的相关性衰减的组合证明的改进版本。
英文摘要：
Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap $ε$ has correlation length $ξ$ upper bounded as $ξ=O(1/ε)$. In general this bound cannot be improved. Here we study the scaling of the correlation length as a function of the spectral gap in frustration-free local Hamiltonians, and we prove a tight bound $ξ=O(1/\sqrtε)$ in this setting. This highlights a fundamental difference between frustration-free and frustrated systems near criticality. The result is obtained using an improved version of the combinatorial proof of correlation decay due to Aharonov, Arad, Vazirani, and Landau.
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