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arXiv · 2206.00027

Modular Commutators in Conformal Field Theory

Yijian Zou·Bowen Shi·Jonathan Sorce·Ian T. Lim·Isaac H. Kim
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Abstract

The modular commutator is a recently discovered multipartite entanglement measure 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.

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Yijian Zou, Bowen Shi, Jonathan Sorce, Ian T. Lim, Isaac H. Kim. 2022-06-14. Modular Commutators in Conformal Field Theory. https://doi.org/10.1103/physrevlett.129.260402

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