Quantum quenches in free field theory: universal scaling at any rate

Sumit R Das,Damián A Galante,Robert C Myers

doi:10.1007/jhep05(2016)164

Sumit R Das, Damián A Galante + Show 1 more

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https://doi.org/10.1007/jhep05(2016)164

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Abstract

Quantum quenches display universal scaling in several regimes. For quenches which start from a gapped phase and cross a critical point, with a rate slow compared to the initial gap, many systems obey Kibble-Zurek scaling. More recently, a different scaling behaviour has been shown to occur when the quench rate is fast compared to all other physical scales, but still slow compared to the UV cutoff. We investigate the passage from fast to slow quenches in scalar and fermionic free field theories with time dependent masses for which the dynamics can be solved exactly for all quench rates. We find that renormalized one point functions smoothly cross over between the regimes.

Highlights

The original arguments of Kibble and Zurek [1, 2] are readily adapted to argue that immediately after the quench, i.e., after entering the non-adiabatic regime, the expectation value of an operator O∆ of dimension ∆ will exhibit universal scaling of the form
We will use the exact mode solutions described in the previous section to provide both analytic and numerical evidence that slow quenches going through a critical point exhibit KZ scaling near the critical point
We will be able to evaluate the corresponding expectation values at a fixed finite time, and by varying the quench rate, 1/δt, we will show a smooth transition from the fast quench regime to the the Kibble-Zurek regime and to the adiabatic regime

Summary

Introduction

The original arguments of Kibble and Zurek [1, 2] (which were made for thermal transitions) are readily adapted to argue that immediately after the quench, i.e., after entering the non-adiabatic regime, the expectation value of an operator O∆ of dimension ∆ will exhibit universal scaling of the form (e.g., see ref. [3,4,5,6]). The original arguments of Kibble and Zurek [1, 2] (which were made for thermal transitions) are readily adapted to argue that immediately after the quench, i.e., after entering the non-adiabatic regime, the expectation value of an operator O∆ of dimension ∆ will exhibit universal scaling of the form A new scaling behaviour has been found for fast quenches. This scaling was first discovered in holographic studies [17,18,19], but later shown to be a completely general result in any quantum field theory whose UV limit is a conformal field theory [20,21,22]. During the quench process, the renormalized expectation value O∆ ren behaves as δλ O∆ ren ∼ δt2∆−d

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