PIRSA:22100092

Modular commutators in conformal field theory, topological order, and holography

Zou, Y. (2022). Modular commutators in conformal field theory, topological order, and holography. Perimeter Institute. https://pirsa.org/22100092

Zou, Yijian. Modular commutators in conformal field theory, topological order, and holography. Perimeter Institute, Oct. 11, 2022, https://pirsa.org/22100092 

          @misc{ pirsa_PIRSA:22100092,
            doi = {10.48660/22100092},
            url = {https://pirsa.org/22100092},
            author = {Zou, Yijian},
            keywords = {Condensed Matter},
            language = {en},
            title = {Modular commutators in conformal field theory, topological order, and holography},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {oct},
            note = {PIRSA:22100092 see, \url{https://pirsa.org}}
          }

Yijian Zou

Perimeter Institute for Theoretical Physics

Talk number
PIRSA:22100092
Collection
Talk Type
Subject
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.

Zoom link:  https://pitp.zoom.us/j/94069836709?pwd=RlA2ZUsxdXlPTlh2TStObHFDNUY0Zz09