Quantum Quenches in a Holographic Kondo Model

TL;DR

This paper investigates the non-equilibrium dynamics of a holographic Kondo model, analyzing quantum quenches, phase transitions, and critical phenomena using gauge/gravity duality, with focus on impurity screening and relaxation timescales.

Contribution

It introduces a holographic model for the Kondo effect, studying quenches, phase transitions, and critical slowing down within a large N gauge/gravity duality framework.

Findings

Relaxation times are set by the lowest quasinormal modes.

Near criticality, critical exponents satisfy zν=1.

At the phase transition, relaxation exhibits power-law and log-periodic oscillations.

Abstract

We study non-equilibrium dynamics and quantum quenches in a recent gauge/gravity duality model for a strongly coupled system interacting with a magnetic impurity with $SU(N)$ spin. At large $N$, it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS$_2$ and models the impurity screening. We study the time dependence of the condensate induced by quenches of the Kondo coupling. The timescale for equilibration is generically given by the lowest-lying quasinormal mode of the dual gravity model. This mode also governs the formation of the screening cloud, which is obtained as the decrease of impurity degrees of freedom with time. In the condensed phase, the leading quasinormal mode is imaginary and the relaxation of the condensate is over-damped. For quenches whose final state is close to the critical point of the large $N$ phase transition, we study the critical slowing down and obtain the combination of critical exponents $z\nu=1$. When the final state is exactly at the phase transition, we find that the exponential ringing of the quasinormal modes is replaced by a power-law behaviour of the form $\sim t^{-a}\sin(b\log t)$. This indicates the emergence of a discrete scale invariance.