Multipartite entanglement in two-dimensional chiral topological liquids

• URL: http://arxiv.org/abs/2301.07130v1
• Date: Tue, 17 Jan 2023 19:00:26 GMT
• Title: Multipartite entanglement in two-dimensional chiral topological liquids
• Authors: Yuhan Liu, Yuya Kusuki, Jonah Kudler-Flam, Ramanjit Sohal, Shinsei Ryu
• Abstract summary: We use the bulk-boundary correspondence to calculate tripartite entanglement in 2d topological phases. We generalize this to the $p$-vertex state, general rational conformal field theories, and more choices of subsystems.
• Score: 8.713843977199108
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The multipartite entanglement structure for the ground states of two dimensional topological phases is an interesting albeit not well understood question. Utilizing the bulk-boundary correspondence, the calculation of tripartite entanglement in 2d topological phases can be reduced to that of the vertex state, defined by the boundary conditions at the interfaces between spatial regions. In this paper, we use the conformal interface technique to calculate entanglement measures in the vertex state, which include area law terms, corner contributions, and topological pieces, and a possible additional order one contribution. This explains our previous observation of the Markov gap $h = \frac{c}{3} \ln 2$ in the 3-vertex state, and generalizes this result to the $p$-vertex state, general rational conformal field theories, and more choices of subsystems. Finally, we support our prediction by numerical evidence, finding precise agreement.

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