Quantum Quench across a Holographic Critical Point

TL;DR

We address quantum quenches across a holographic critical point using a probe neutral scalar field with mass $m^2$ in a charged $AdS_4$ black brane. The key finding is that near the critical point the dynamics is governed by a single zero mode, enabling a Landau-Ginsburg-type effective theory with a linear-in-time derivative and universal scaling with the quench rate $v$, corroborated by analytic scaling arguments and bulk numerical solutions. The work analyzes two quench protocols—varying the boundary source $J(t)$ at fixed $m^2$ and varying $m^2(t)$ with vanishing source—showing adiabatic breakdown and zero-mode domination in the critical region and linking the exponents to static critical behavior. It highlights how dissipative horizon physics shapes non-equilibrium critical dynamics in holographic settings and outlines directions for extending to zero-temperature BKT-like transitions, Lifshitz IR geometries, inhomogeneous quenches, entanglement entropy, and $1/N$ corrections.

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.

Figures (3)

• Figure 1: The order parameter as a function of time for a $J(t) = \tanh(vt)$ at $m^2=0$ with $v=10^{-0.5},10^{-1},10^{-1.5},10^{-2}$ (from the bottom on the left). The adiabatic solution (dashed) is also shown as a comparison.
• Figure 2: Profile of (rescaled) zero mode ($x^{-\Delta_-} \phi(x)$, where $x\sim {1\over r})$) with $m^2 \approx -2.235$ and $\eta=0.98$.
• Figure 3: A typical response under a continuous but fast change of $m^2(t) \approx -2.1825 (0.9-0.1\tanh (3 t))$. Here $\eta \approx 0.991$ and $m_c^2 \approx -2.169$ at $t=0$.