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DOE OSTI · 2421209

Modular Commutators in Conformal Field Theory

Zou, Yijian·Shi, Bowen·Sorce, Jonathan·Lim, Ian T.·Kim, Isaac H.
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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. Finally, 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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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSChern insulatorsconformal field theoryedge statesentanglement in field theoryfree-electron modelgauge-gravity dualitiesquantum many-body systemstopological superconductors

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Zou, Yijian, Shi, Bowen, Sorce, Jonathan, Lim, Ian T., Kim, Isaac H.. 2022-12-22. Modular Commutators in Conformal Field Theory. https://doi.org/10.1103/physrevlett.129.260402

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