Quantum Quench across a Holographic Critical Point

TL;DR

This paper investigates the non-equilibrium dynamics of a strongly coupled quantum field theory near a critical point using holographic duality, revealing universal scaling behavior and effective Landau-Ginsburg dynamics during a quantum quench.

Contribution

It introduces a holographic model for quantum quenches across a critical point, deriving effective Landau-Ginsburg dynamics and scaling laws for the order parameter.

Findings

Zero mode dominates the dynamics near criticality.

The order parameter drops to zero at a delayed time $t_\star$.

Numerical results confirm the predicted scaling behavior.

Abstract

We study the problem of quantum quench across a critical point in a strongly coupled field theory using AdS/CFT techniques. The model involves a probe neutral scalar field with mass-squared $m^2$ in the range $-9/4 < m^2 < -3/2$ in a $AdS_4$ charged black brane background. For a given brane background there is a critical mass-squared, $m_c^2$ such that for $m^2 < m_c^2$ the scalar field condenses. The theory is critical when $m^2 = m_c^2$ and the source for the dual operator vanishes. At the critical point, the radial operator for the bulk linearized problem has a zero mode. We study the dynamics of the order parameter with a time dependent source $J(t)$, or a null-time dependent bulk mass $m(u)$ across the critical point. We show that in the critical region the dynamics for an initially slow variation is dominated by the zero mode : this leads to an effective description in terms of a Landau-Ginsburg type dynamics with a {\em linear} time derivative. Starting with an adiabatic initial condition in the ordered phase, we find that the order parameter drops to zero at a time $t_\star$ which is later than the time when $(m_c^2-m^2)$ or $J$ hits zero. In the critical region, $t_\star$, and the departure of the order parameter from its adiabatic value, scale with the rate of change, with exponents determined by static critical behavior. Numerical results for the order parameter are consistent with these expectations.