Title: Holographic Butterfly Effect and Diffusion in Quantum Critical Region,
Abstract: We investigate the butterfly effect and charge diffusion near the quantum
phase transition in holographic approach. We argue that their criticality is
controlled by the holographic scaling geometry with deformations induced by a
relevant operator at finite temperature. Specifically, in the quantum critical
region controlled by a single fixed point, the butterfly velocity decreases
when deviating from the critical point. While, in the non-critical region, the
behavior of the butterfly velocity depends on the specific phase at low
temperature. Moreover, in the holographic Berezinskii-Kosterlitz-Thouless
transition, the universal behavior of the butterfly velocity is absent.
Finally, the tendency of our holographic results matches with the numerical
results of Bose-Hubbard model. A comparison between our result and that in the
$O(N)$ nonlinear sigma model is also given.