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Universality in fast quantum quenches

Nov 27, 2014

83 pages

Published in:

JHEP 02 (2015) 167

Published: Feb 26, 2015

e-Print:

1411.7710 [hep-th]

DOI:

10.1007/JHEP02(2015)167

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Abstract: (Springer)

We expand on the investigation of the universal scaling properties in the early time behaviour of fast but smooth quantum quenches in a general d-dimensional conformal field theory deformed by a relevant operator of dimension Δ with a time-dependent coupling. The quench consists of changing the coupling from an initial constant value λ

_{1}

by an amount of the order of δλ to some other final value λ

_{2}

, over a time scale δt. In the fast quench limit where δt is smaller than all other length scales in the problem, δt ≪ λ_{1}^{1/(}^{Δ − d}^{)} , λ_{2}^{1/(}^{Δ − d}^{)} , δλ^{1/(}^{Δ − d}^{)}, the energy (density) injected into the system scales as δℰ ∼ (δλ)

^{2}

(δt)^{d}^{− 2}^{Δ} . Similarly, the change in the expectation value of the quenched operator at times earlier than the endpoint of the quench scales as

\left\langle {\mathcal{O}}_{\varDelta}\right\rangle \sim \delta \lambda {{\left(\delta t\right)}^d}^{-2\varDelta }

, with further logarithmic enhancements in certain cases. While these results were first found in holographic studies, we recently demonstrated that precisely the same scaling appears in fast mass quenches of free scalar and free fermionic field theories. As we describe in detail, the universal scaling refers to renormalized quantities, in which the UV divergent pieces are consistently renormalized away by subtracting counterterms derived with an adiabatic expansion. We argue that this scaling law is a property of the conformal field theory at the UV fixed point, valid for arbitrary relevant deformations and insensitive to the details of the quench protocol. Our results highlight the difference between smooth fast quenches and instantaneous quenches where the Hamiltonian abruptly changes at some time.

Note:

83 pages, lots of figures; v2: minor modifications to match published version; v3: typo correction

Gauge-gravity correspondence
Effective field theories
Holography and condensed matter physics (AdS/CMT)
field theory: conformal
mass: quenching
field theory: deformation
fermion: field theory
coupling: time dependence
expansion: adiabatic
operator: dimension

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