Slow relaxation and diffusion in holographic quantum critical phases

Understand

The dissipative dynamics of strongly interacting systems are often characterised by the timescale set by the inverse temperature $\tau_P\sim\hbar/(k_BT)$.

• We show that near a class of strongly interacting quantum critical points that arise in the infra-red limit of translationally invariant holographic theories, there is a collective excitation (a quasinormal mode of the dual black hole spacetime) whose lifetime $\tau_{eq}$ is parametrically longer than $\tau_P$: $\tau_{eq}\gg T^{-1}$.
• The lifetime is enhanced due to its dependence on a dangerously irrelevant coupling that breaks the particle-hole symmetry and the invariance under Lorentz boosts of the quantum critical point.
• The thermal diffusivity (in units of the butterfly velocity) is anomalously large near the quantum critical point and is governed by $\tau_{eq}$ rather than $\tau_P$.