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Modular Commutators in Conformal Field Theory.

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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… Click to show full abstract

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.

Keywords: conformal field; commutator; modular commutator; modular commutators; commutators conformal

Journal Title: Physical review letters
Year Published: 2022

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