论文标题
Lieb-Robinson的边界意味着互动的位置
Lieb-Robinson bounds imply locality of interactions
论文作者
论文摘要
离散的晶格模型是量子多体物理学的基石。它们是对凝结物质系统和晶格登记量子场理论的有效描述的出现。 Lieb-Robinson的边界表明，如果每个晶格位点的自由度仅在本地相互作用，则相关性只能通过晶格与有限的群体速度传播，类似于相对论系统中的光锥。在这里，我们表明Lieb-Robinson界限等于相互作用的局部性：具有K-Body交互的系统在且仅当基础相互作用在空间中呈指数衰减时，以指数形式满足Lieb-Robinson的界限。特别是，我们的结果已经遵循单位可观察物的两点相关函数的行为，并将其推广到不同的衰减行为以及费米子晶格模型。因此，我们发现单点可观察物的Lieb-Robinson界限暗示着有限的可观察到的Lieb-Robinson边界，并具有任意支持。
Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of freedom at each lattice site only interact locally with each other, correlations can only propagate with a finite group velocity through the lattice, similarly to a light cone in relativistic systems. Here we show that Lieb-Robinson bounds are equivalent to the locality of the interactions: a system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. In particular, our result already follows from the behavior of two-point correlation functions for single-site observables and generalizes to different decay behaviours as well as fermionic lattice models. As a side-result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for bounded observables with arbitrary support.
