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首页> 外文期刊>Physical review >Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations
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Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations

机译：面积法及其违反：对纠缠和波动结构的微观检查

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摘要

Quantum fluctuations of local quantities can be a direct signature of entanglement in an extended quantum many-body system. Hence they may serve as a theoretical (as well as an experimental) tool to detect the spatial properties of the entanglement entropy of a subsystem-more specifically, its scaling with the size of the subsystem itself. In the ground state of quantum many-body systems, this scaling is typically linear in the boundary of the subsystem (area law), with at most multiplicative logarithmic corrections. Here we propose a microscopic insight into the spatial structure of entanglement and particle-number fluctuations using the concept of contour, recently introduced to decompose the bipartite entanglement entropy of lattice free fermions between two extended regions A and B into contributions from single sites in A. We generalize the notion of contour to the entanglement of any quadratic (bosonic or fermionic) lattice Hamiltonian, as well as to particle-number fluctuations. The entanglement and fluctuations contours are found to generally decay when moving away from the boundary between A and B. We show that in the case of free fermions the decay of the entanglement contour follows closely that of the fluctuation contour: this establishes a microscopic link between the scaling of entanglement and that of particle-number fluctuations, and it allows us to predict the presence (or violation) of entanglement area laws solely based on the density-density correlation function. In the case of Bose-condensed interacting bosons, treated via the Bogoliubov and spin-wave approximations, such a link cannot be established-fluctuation and entanglement contours are found to be radically different, as they lead to a logarithmically violated area law for particle-number fluctuations, and to a strict area law of entanglement. Analyzing in depth the role of the zero-energy Goldstone mode of spin-wave theory, and of the corresponding lowest-energy mode in the entanglement spectrum, we unveil a subtle interplay between the special contour and energy scaling of the latter, and universal additive logarithmic corrections to entanglement area law discussed extensively in the recent literature.
机译：局部量的量子涨落可以是扩展的量子多体系统中纠缠的直接特征。因此，它们可以用作理论（以及实验）工具，以检测子系统的纠缠熵的空间属性，更具体地说，可以根据子系统本身的大小进行缩放。在量子多体系统的基态下，这种缩放比例通常在子系统的边界（面积定律）中是线性的，最多具有乘法对数校正。在这里，我们使用等高线的概念对缠结和粒子数波动的空间结构提出了微观的见解，最近将其引入来将两个扩展区域A和B之间的无晶格费米子的二分纠缠熵分解为A中单个位置的贡献。我们将轮廓的概念推广到任何二次（正弦或费米子）晶格哈密顿量的纠缠以及粒子数波动。当远离A和B的边界时，发现纠缠和涨落等高线通常会衰减。我们表明，在自由费米子的情况下，纠缠等高线的衰减与涨落等高线密切相关：这在两者之间建立了微观联系。纠缠的尺度和粒子数波动的尺度，它使我们能够仅基于密度-密度相关函数来预测纠缠面积定律的存在（或违反）。在玻色凝聚的玻色子中，通过Bogoliubov和自旋波近似处理，无法建立这样的联系-波动和纠缠等高线根本不同，因为它们导致对数违背了粒子-粒子的面积定律。数量的波动，并以严格的面积纠缠定律。深入分析自旋波理论的零能量戈德斯通模式以及纠缠谱中相应的最低能量模式的作用，我们揭示了后者的特殊轮廓和能量缩放以及通用加性之间的微妙相互作用。对纠缠面积定律的对数校正在最近的文献中已广泛讨论。

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