Signature of quantum chaos in operator entanglement in 2d CFTs

We study operator entanglement measures of the unitary evolution operators of
(1+1)-dimensional conformal field theories (CFTs), aiming to uncover their scrambling
and chaotic behaviors. In particular, we compute the bi-partite and tri-partite mutual
information for various configurations of input and output subsystems, and as a function of time.
We contrast three different CFTs: the free fermion theory, compactified
free boson theory at various radii, and CFTs with holographic dual.
We found that the bi-partite mutual information exhibits distinct behaviors for these different CFTs,
reflecting the different information scrambling capabilities of these unitary operators;
while a quasi-particle picture can describe well the case the free fermion and free boson
CFTs, it completely fails for the case of holographic CFTs. Similarly, the tri-partite
mutual information also distinguishes the unitary evolution operators of different CFTs.
In particular, its late-time behaviors, when the output subsystems are semi-infinite, are
quite distinct for these theories. We speculate that for holographic theories the late-
time saturation value of the tri-partite mutual information takes the largest possible
negative value and saturates the lower bound among quantum field theories.