Multipartite entanglement in two-dimensional chiral topological liquids

TL;DR

This paper investigates the multipartite entanglement structure of ground states in 2D topological liquids, using conformal interface techniques to compute entanglement measures and verify theoretical predictions with numerical evidence.

Contribution

It introduces a method to calculate multipartite entanglement in 2D topological phases via boundary conformal interfaces, extending previous results and providing numerical validation.

Findings

Calculation of entanglement measures including topological contributions

Generalization of Markov gap to p-vertex states and rational CFTs

Numerical evidence supporting theoretical predictions

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.