Holographic quenches towards a Lifshitz point

TL;DR

This paper investigates holographic quantum quenches towards a Lifshitz fixed point, showing that such quenches lead to black hole formation and a top-down equilibration process in a strongly coupled theory.

Contribution

It demonstrates how holographic duality can model quenches towards Lifshitz points and reveals the dynamical formation of black holes and the nature of equilibration in these systems.

Findings

Asymptotically Lifshitz black holes form after quenches.

Reaching the Lifshitz vacuum state from CFT vacuum is impossible.

Symmetry breaking occurs faster for UV modes, indicating top-down equilibration.

Abstract

We use the holographic duality to study quantum quenches of a strongly coupled CFT that drive the theory towards a non-relativistic fixed point with Lifshitz scaling. We consider the case of a Lifshitz dynamical exponent $z$ close to unity, where the non-relativistic field theory can be understood as a specific deformation of the corresponding CFT and, hence, the standard holographic dictionary can be applied. On the gravity side this amounts to finding a dynamical bulk solution which interpolates between AdS and Lishitz spacetimes as time evolves. We show that an asymptotically Lifshitz black hole is always formed in the final state. This indicates that it is impossible to reach the vacuum state of the Lifshitz theory from the CFT vacuum as a result of the proposed quenching mechanism. The nonequilibrium dynamics following the breaking of the relativistic scaling symmetry is also probed using both local and non-local observables. In particular, we conclude that the equilibration process happens in a top-down manner, i.e., the symmetry is broken faster for UV modes.