Thermalization in 2D critical quench and UV/IR mixing

Gautam Mandal; Shruti Paranjape; Nilakash Sorokhaibam

paper

Thermalization in 2D critical quench and UV/IR mixing

arXiv:1512.02187

Abstract

We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass $m (t)$ that goes from $m_{0}$ to zero. We prove that, as anticipated in MSS \cite{Mandal:2015jla}, the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form $∣ ψ ⟩$ = $exp [- κ_{2} H - \sum_{n > 2}^{\infty} κ_{n} W_{n}] ∣Bd ⟩$ . The $W_{n}$ ( $n = 2, 3, ...$ , $W_{2} = H$ ) here represent the conserved $W_{\infty}$ charges and $∣Bd ⟩$ represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the $κ_{n}$ 's as in MSS. We compute exact time-dependent correlators for some specific quench protocols $m (t)$ . The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature $β = 4 κ_{2}$ , and chemical potentials $μ_{n} = 4 κ_{n}$ . In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol $m (t)$ from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all $κ_{n}$ 's, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.

Published version, a minor correction in eqn(41)

Thermalization in 2D critical quench and UV/IR mixing

Abstract

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