Multipartite entanglement and quantum Fisher information in conformal field theories

The bipartite entanglement entropy of a segment of length l in 1+1-dimensional conformal field theories (CFT) follows the formula S=c3lnl+γ, where c is the central charge of the CFT and γ is a cutoff-dependent constant which diverges in the absence of an ultraviolet cutoff. According to this formula, systems with larger central charges have more bipartite entanglement entropy. Using quantum Fisher information (QFI), we argue that systems with bigger central charges not only have larger bipartite entanglement entropy, but also have more multipartite entanglement content. In particular, we argue that since a system with a smaller smallest scaling dimension has a larger QFI, the multipartite entanglement content of a CFT is dependent on the value of the smallest scaling dimension present in the spectrum of the system. We show that our argument seems to be consistent with some of the existing results regarding the von Neumann entropy, negativity, and localizable entanglement in 1+1 dimensions. Furthermore, we also argue that the QFI decays under renormalization group flow between two unitary CFTs. Finally, we also comment on nonconformal but scale-invariant systems.