Slow relaxation and diffusion in holographic quantum critical phases

TL;DR

This paper investigates slow relaxation and diffusion in holographic quantum critical phases, revealing a long-lived collective mode influenced by dangerously irrelevant couplings, with implications for thermal diffusivity and scaling behavior.

Contribution

It demonstrates the existence of a long-lived collective excitation near certain quantum critical points in holographic theories, linked to dangerously irrelevant couplings affecting equilibration times.

Findings

Existence of a quasinormal mode with lifetime much longer than inverse temperature

Thermal diffusivity governed by the long-lived mode rather than temperature

Scaling theory extended to include dangerously irrelevant couplings

Abstract

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 $\tau_P$. We conjecture that there exists a long-lived, propagating collective mode with velocity $v_s$, and in this case the relation $D=v_s^2\tau_{eq}$ holds exactly in the limit $T\tau_{eq}\gg1$. While scale invariance is broken, a generalised scaling theory still holds provided that the dependence of observables on the dangerously irrelevant coupling is incorporated. Our work further underlines the connection between dangerously irrelevant deformations and slow equilibration.