Holographic butterfly effect and diffusion in quantum critical region

• Published in: The journal of high energy physics Vol. 2017; no. 9; pp. 1 - 34
• Main Authors: Ling, Yi, Xian, Zhuo-Yu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2017; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes; Classical and Quantum Gravitation; Critical point; Deformation; Diffusion effects; Elementary Particles; High energy physics; Holography and condensed matter physics (AdS/CMT); Mathematical models; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; AdS-CFT Correspondence; Holography and condensed matter physics (AdS/CMT); Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2017)003

A bstract 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.