Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

• Main Authors: Hyun-Sik Jeong, Keun-Young Kim, Ya-Wen Sun
• Format: Article
• Language: English
• Published: SpringerOpen 2021-07-01
• Series: Journal of High Energy Physics
• Subjects: Holography and condensed matter physics (AdS/CMT); Gauge-gravity correspondence
• Online Access: https://doi.org/10.1007/JHEP07(2021)105

Abstract We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent (λ L ) and butterfly velocity (v B ), independently of the symmetry breaking patterns. We show that the diffusion constant (D) is bounded by D ≥ v B 2 / λ L $$ D\ge {v}_B^2/{\lambda}_L $$ , where D is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.