Modular Commutators in Conformal Field Theory
Modular Commutators in Conformal Field Theory
复制标题
共形场论中的模块化换向器
DOI：
10.1103/physrevlett.129.260402
复制
发表时间：
2022
影响因子：
8.6
通讯作者：
Kim, Isaac H.
中科院分区：
文献类型：
--
作者：
Zou, Yijian;Shi, Bowen;Sorce, Jonathan;Lim, Ian T.;Kim, Isaac H.
模交换子是最近发现的一种纠缠量，它量化了多体量子态的手征性。在这封信中，我们导出了共形场论中模交换子在维数上的普遍表达式，并讨论了它的显著特征。我们证明了模交换子只依赖于手征中心荷和共形交比。我们测试了这个公式的间隙（）维系统的手征边缘，即，的量子霍尔态，并观察到良好的协议与数值模拟。此外，我们提出了一个几何对偶的模交换子在某些优选状态的AdS/CFT对应。对于这些状态，我们认为，模块交换子可以从一组相交的Ryu-Takayanagi表面之间的交叉角。
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 indimensions 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 ()-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.