标题： 二维共形场论中的子系统熵和KdV ETH 显示英文标题

标题： Subsystem entropy in 2d CFT and KdV ETH

摘要： 我们研究二维共形场论中的子系统熵，其中子系统构成整个系统的有限部分。 我们关注其广延贡献，在热力学极限下，该贡献与子系统大小成线性比例。 我们采用所谓的对角近似来评估混沌共形场论在热态（规范系综）、微正则系综和初级态下的子系统熵，结果与之前已知的结果一致。 然后，我们继续寻找在全局共形场论态为KdV广义吉布斯系综或KdV微正则系综时，子系统熵在$c$的领先阶的解析表达式。 先前对初级本征态的研究表明，类似于AdS/CFT中的固定面积态，对应的子系统纠缠谱是平坦的。 这种行为似乎与热（微正则）态的行为形成尖锐矛盾，因此显然与子系统本征态热化假设（ETH）相矛盾。 在本工作中，我们通过将初级态与KdV（微）正则系综进行比较来解决这一问题。 我们证明结果与子系统ETH的KdV推广版本一致，在该版本中，量子本征态的局部性质由其守恒KdV电荷的值所支配。 我们的工作加强了二维共形场论中KdV推广的ETH的证据，并强调了Renyi熵作为对约化密度矩阵的敏感探测器。 显示英文摘要

摘要： We study subsystem entropy in 2d CFTs, for subsystems constituting a finite fraction of the full system. We focus on the extensive contribution, which scales linearly with the subsystem size in the thermodynamic limit. We employ the so-called diagonal approximation to evaluate subsystem entropy for the chaotic CFTs in thermal state (canonical ensemble), microcanonical ensemble, and in a primary state, matching previously known results. We then proceed to find analytic expressions for the subsystem entropy at leading order in $c$, when the global CFT state is the KdV generalized Gibbs ensemble or the KdV microcanonical ensemble. Previous studies of primary eigenstates have shown that, akin to fixed-area states in AdS/CFT, corresponding subsystem entanglement spectrum is flat. This behavior is seemingly in sharp contradiction with the one for the thermal (microcanonical) state, and thus in apparent contradiction with the subsystem Eigenstate Thermalization Hypothesis (ETH). In this work, we resolve this issue by comparing the primary state with the KdV (micro)canonical ensemble. We show that the results are consistent with the KdV-generalized version of the subsystem ETH, in which local properties of quantum eigenstates are governed by their values of conserved KdV charges. Our work solidifies evidence for the KdV-generalized ETH in 2d CFTs and emphasizes Renyi entropy as a sensitive probe of the reduced-density matrix.