Quantum Quenches in a Holographic Kondo Model

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.

23 pages + appendices, 11 figures

References in corpus (11)

• Fractionalized Fermi liquids
• Hydrodynamics of Holographic Superconductors
• Universal far-from-equilibrium Dynamics of a Holographic Superconductor
• Non-equilibrium Condensation Process in a Holographic Superconductor
• Universal quench dynamics of interacting quantum impurity systems
• Dynamic critical phenomena in the AdS/CFT duality
• Multi-scale fluctuations near a Kondo Breakdown Quantum Critical Point
• Nonequilibrium, spatio-temporal formation of the Kondo screening-cloud on a lattice
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Critical phenomena in the AdS/CFT duality
• Real-time dynamics induced by quenches across the quantum critical points in gapless Fermi systems with a magnetic impurity

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• Time evolution of entanglement for holographic steady state formation
• Conformal field theory analysis for QCD Kondo effect
• Discrete scale invariance in holography revisited
• Non-equilibrium dynamics in Holography
• Chaotic Correlation Functions with Complex Fermions
• Encoded information of mixed correlations: the views from one dimension higher
• Holographic RG Flows for Kondo-like Impurities
• Introduction to Gauge/Gravity Duality (TASI Lectures 2017)
• Critical and near-critical relaxation of holographic superfluids
• Holographic Superconductors: An Analytic Method Revisit
• Holographic mean field theory and Kondo lattice