Holographic Butterfly Effect and Diffusion in Quantum Critical Region

TL;DR

This paper explores how the butterfly effect and charge diffusion behave near quantum phase transitions using holographic models, revealing critical dependencies and contrasting behaviors across different regions and models.

Contribution

It introduces a holographic framework to analyze the critical behavior of butterfly velocity and diffusion near quantum phase transitions, including BKT transitions.

Findings

Butterfly velocity decreases away from critical points in the quantum critical region.

Behavior of butterfly velocity varies depending on the phase in non-critical regions.

Universal behavior of butterfly velocity is absent in holographic BKT transitions.

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.