Zou Yijian, Shi Bowen, Sorce Jonathan, Lim Ian T, Kim Isaac H
Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA.
Department of Physics, University of California at San Diego, La Jolla, California 92093, USA.
Phys Rev Lett. 2022 Dec 23;129(26):260402. doi: 10.1103/PhysRevLett.129.260402.
The modular commutator is a recently discovered entanglement quantity that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in conformal field theories in 1+1 dimensions and discuss its salient features. We show that the modular commutator depends only on the chiral central charge and the conformal cross ratio. We test this formula for a gapped (2+1)-dimensional system with a chiral edge, i.e., the quantum Hall state, and observe excellent agreement with numerical simulations. Furthermore, we propose a geometric dual for the modular commutator in certain preferred states of the AdS/CFT correspondence. For these states, we argue that the modular commutator can be obtained from a set of crossing angles between intersecting Ryu-Takayanagi surfaces.
模块化对易子是最近发现的一种纠缠量，它量化了底层多体量子态的手征性。在本信函中，我们推导了1 + 1维共形场论中模块化对易子的通用表达式，并讨论了其显著特征。我们表明，模块化对易子仅取决于手征中心荷和共形交叉比。我们对具有手征边缘的带隙（2 + 1）维系统（即量子霍尔态）测试了此公式，并观察到与数值模拟的极佳一致性。此外，我们为AdS/CFT对应关系的某些优选态提出了模块化对易子的几何对偶。对于这些态，我们认为模块化对易子可以从相交的Ryu - Takayanagi曲面之间的一组交叉角获得。
