# Geometric contribution to entanglement entropy and multipartite entanglement in two-dimensional chiral topological liquid

### APA

Liu, Y. (2022). Geometric contribution to entanglement entropy and multipartite entanglement in two-dimensional chiral topological liquid . Perimeter Institute. https://pirsa.org/22110059

### MLA

Liu, Yuhan. Geometric contribution to entanglement entropy and multipartite entanglement in two-dimensional chiral topological liquid . Perimeter Institute, Nov. 30, 2022, https://pirsa.org/22110059

### BibTex

@misc{ pirsa_PIRSA:22110059, doi = {10.48660/22110059}, url = {https://pirsa.org/22110059}, author = {Liu, Yuhan}, keywords = {Condensed Matter}, language = {en}, title = {Geometric contribution to entanglement entropy and multipartite entanglement in two-dimensional chiral topological liquid }, publisher = {Perimeter Institute}, year = {2022}, month = {nov}, note = {PIRSA:22110059 see, \url{https://pirsa.org}} }

Yuhan Liu University of Chicago

## 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 tripartite entanglement calculation of 2d topological phases can be reduced to that on the vertex state, defined by the boundary conditions at the interfaces between spatial regions. In this work, we use the conformal interface technique to calculate the entanglement measures of the vertex state, which include the area-law, geometrical and topological pieces, and the possible extra order one contribution. This explains our previous observation of Markov gap h=\frac{c}{3}\ln 2 in the 3-vertex state, and generalizes it to the p-vertex state as well as rational conformal field theory, and more general choices of subsystem. Finally, we support our prediction by numerical evidence.

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