Miao Qiang, Barthel Thomas
Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Phys Rev Lett. 2021 Jul 23;127(4):040603. doi: 10.1103/PhysRevLett.127.040603.
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≤3 dimensions and have also been confirmed for bosonic systems and nonintegrable spin chains.
对于服从本征态热化假设（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一个单一的交叉函数描述。ETH 意味着交叉函数可以从热系综的子系统熵推导出来，并且具有普适性质。这些函数捕捉了从低能量和小子系统尺寸（面积或对数面积律）下的基态纠缠区域到高能量或大子系统尺寸下的广延体积律区域的完整交叉。对于临界一维系统，共形场论给出了一个普适标度函数，并且可以适用于非线性色散情况。我们用它来推导 d > 1 维费米液体的交叉标度函数。对于 d ≤ 3 维的大型非相互作用费米子系统，数值计算补充了分析结果，并且对于玻色子系统和不可积自旋链也得到了证实。
