Dr Masahiro Nozaki (RIKEN)
We study operator entanglement measures of the unitary evolution operators of (1+1)-dimensional conformal field theories, aiming to uncover scrambling and chaotic behaviors thereof. In particular, we compute the bi-partite and tri-partite mutual in- formation for various configurations of input and output subsystems, and as a function of time. We contrast three different conformal field theories: the free fermion the- ory, compactified free boson theory at various radii, and conformal field theories with holographic dual. We found that the bi-partite mutual information exhibits distinct behaviors for these different conformal field theories, reflecting the different informa- tion scrambling abilities of these unitary operators; while a quasi-particle picture can describe well the case of the free fermion and free boson conformal field theories, it completely fails for the case of holographic conformal field theories. Similarly, the tripartite mutual information also distinguishes the unitary evolution operators of dif- ferent conformal field theories. In particular, the late time behaviors of the tripartite mutual information, when the output subsystems are semi-infinite, are quite distinct for the free fermion conformal field theory, the free boson theory at different compacti- fication radii, and holographic conformal field theories. We speculate that the late time saturation value of the tripartite information for holographic conformal field theories saturates the lower bound of the negativity of the tripartite mutual information.