We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the correlation length, the average entanglement follows a subthermal volume law, whose coefficient is a universal scaling function. The full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump at the transition from fully thermal volume law on the thermal side, to pure area law on the MBL side.

中文翻译：

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多主体本地化转变中的纠缠度定标理论

我们研究了本征态纠缠熵在多体局部（MBL）和热相之间的跃迁的通用性质。我们开发了一种改进的实空间重归一化组方法，该方法可以对大型系统尺寸进行数值模拟，并可以对无限的系统尺寸极限进行系统外推。对于小于相关长度的系统，平均纠缠遵循亚热体积定律，其系数为通用比例函数。纠缠的完全分布遵循通用缩放形式，并且呈现出双峰结构，该双峰结构可生成对主导体积定律的普遍次主导幂定律校正。对于大于相关长度的系统，短间隔纠缠在热侧从完全热体积定律的过渡处表现出不连续的跳跃，