Quantum Quench and Double Trace Couplings

TL;DR

This paper investigates quantum quenches in strongly coupled field theories with gravity duals, revealing critical phase transitions and Kibble-Zurek scaling behavior in different backgrounds, with analytical and numerical support.

Contribution

It introduces a holographic model for quantum quenches crossing critical points, analyzing dynamics with a Landau-Ginsburg equation and identifying different dynamical exponents.

Findings

Critical phase transition at negative double trace coupling

Kibble-Zurek scaling in non-equilibrium dynamics

Different dynamical critical exponents for backgrounds

Abstract

We consider quantum quench by a time dependent double trace coupling in a strongly coupled large N field theory which has a gravity dual via the AdS/CFT correspondence. The bulk theory contains a self coupled neutral scalar field coupled to gravity with negative cosmological constant. We study the scalar dynamics in the probe approximation in two backgrounds: AdS soliton and AdS black brane. In either case we find that in equilibrium there is a critical phase transition at a {\em negative} value of the double trace coupling $\kappa$ below which the scalar condenses. For a slowly varying homogeneous time dependent coupling crossing the critical point, we show that the dynamics in the critical region is dominated by a single mode of the bulk field. This mode satisfies a Landau-Ginsburg equation with a time dependent mass, and leads to Kibble Zurek type scaling behavior. For the AdS soliton the system is non-dissipative and has $z=1$, while for the black brane one has dissipative $z=2$ dynamics. We also discuss the features of a holographic model which would describe the non-equilibrium dynamics around quantum critical points with arbitrary dynamical critical exponent $z$ and correlation length exponent $\nu$. These analytical results are supported by direct numerical solutions.