Universal Scaling in Fast Quantum Quenches in Conformal Field Theories

Abstract

We study the time evolution of a conformal field theory deformed by a relevant operator under a smooth but fast quantum quench which brings it to the conformal point. We argue that when the quench time scale δt is small compared to the scale set by the relevant coupling, the expectation value of the quenched operator scales universally as δλ/δt 2∆−d where δλ is the quench amplitude. This growth is further enhanced by a logarithmic factor in even dimensions. We present explicit results for free scalar and fermionic field theories, supported by an analytic understanding of the leading contribution for fast quenches. Results from this Letter suggest that this scaling result, first found in holography, is in fact universal to quantum quenches. Our considerations also show that this limit of fast smooth quenches is quite different from an instantaneous quench from one time-independent Hamiltonian to another, where the Schrodinger picture state at the time of the quench simply serves as an initial condition for subsequent evolution with the final Hamiltonian.

Weak field collapse in AdS: introducing a charge density

“…Note that, this scaling is in keeping with the scaling behaviour obtained in [47][48][49], which follows from dimensional analysis in our case. Evidently, (4.39) provides us with a natural meaning for the expansion parameter in gravity purely in terms of the field theory data.…”

Kibble-Zurek scaling in holographic quantum quench: backreaction

“…More recently [18,19] have studied the problem by modelling these fluctuations with a noise in the time evolution in a manner consistent with the fluctuationdissipation theorem and found consistency with the Kibble Zurek mechanism. Other aspects of quantum quench which involve critical points have been investigated in [20][21][22][23][24][25][26][27][28][29][30].…”

“…The derivative expansions for the various fields are 30) where ǫ is the adiabaticity parameter and the lowest order solutions are obtained from the static solutions by replacing the constant source J by the time dependent source J(t),…”

Equilibration and GGE in interacting-to-free quantum quenches in dimensions $d\gt 1$

“…A natural extension to supersymmetric models would be to consider supersymmetric initial states [98] where powerful tools such as localisation [99] are available. Another approach studied extensively is based on the AdS/CFT correspondence [83,[100][101][102][103][104][105][106][107] where equilibration is thermal. An interesting open question is: if a thermal ensemble is described in this context by a black hole, what is the gravitydual of a GGE ensemble?…”