Eigenstate Entanglement: Crossover from the Ground State to Volume Laws,Physical Review Letters

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Eigenstate Entanglement: Crossover from the Ground State to Volume Laws
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-07-21 , DOI: 10.1103/physrevlett.127.040603
Qiang Miao ₁ , Thomas Barthel ₁

Affiliation

For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that the crossover functions can be deduced from subsystem entropies of thermal ensembles and have universal properties. These functions capture the full crossover from the ground-state entanglement regime at low energies and small subsystem size (area or log-area law) to the extensive volume-law regime at high energies or large subsystem size. For critical one-dimensional systems, a universal scaling function follows from conformal field theory and can be adapted for nonlinear dispersions. We use it to also deduce the crossover scaling function for Fermi liquids in

d > 1

dimensions. The analytical results are complemented by numerics for large noninteracting systems of fermions in

d \leq 3

dimensions and have also been confirmed for bosonic systems and nonintegrable spin chains.

中文翻译：

本征态纠缠：从基态到体积定律的交叉

对于遵循本征态热化假设 (ETH) 的典型量子多体系统，我们认为（几乎）所有能量本征态的纠缠熵都由单个交叉函数描述。ETH 意味着交叉函数可以从热系综的子系统熵中推导出来，并且具有通用属性。这些函数捕获了从低能量和小子系统尺寸（面积或对数面积定律）的基态纠缠状态到高能量或大子系统尺寸的广泛体积定律状态的完全交叉。对于关键的一维系统，通用标度函数遵循共形场理论，可以适用于非线性色散。我们还用它来推导出费米液体的交叉标度函数