Quantum Revivals in Conformal Field Theories in Higher Dimensions

Abstract

We investigate the behavior of the return amplitude $\mathcal{F}(t)=|⟨\Psi (0)|\Psi (t)⟩|$ following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension $d-1$ and linear size $O(L)$, from a state $|\Psi (0)⟩$ of extensive energy with short-range correlations. After an initial gaussian decay $\mathcal{F}(t)$ reaches a plateau value related to the density of available states at the initial energy. However for $d=3,4$ this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least $O({\sigma }^{1/(d-1)}L)$, where $\sigma \gg 1$ is the dimensionless Stefan-Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times $t\sim\mbox{integer}\times L$. In particular, on a sphere $S_{d-1}$ of circumference $2\pi L$, there is an action of the modular group on $\mathcal{F}(t)$ implying structure near all rational values of $t/L$, similarly to what happens for rational CFTs in $d=2$.

19 pages, 14 figures. v2: minor error corrected

References in corpus (18)

• The Luttinger model following a sudden interaction switch-on
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Dephasing and the steady state in quantum many-particle systems
• Quantum quenches in 1+1 dimensional conformal field theories
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Generalized Thermalization in an Integrable Lattice System
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Thermalization of Strongly Coupled Field Theories
• Holographic Evolution of Entanglement Entropy
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Gauge/gravity duality and thermalization of a boost-invariant perfect fluid
• Thermalization and Revivals after a Quantum Quench in Conformal Field Theory
• Large deviations and universality in quantum quenches
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Synchronous Optical Pumping of Quantum Revival Beats for Atomic Magnetometery

Cited by in corpus (10)

• Quantum quenches in 1+1 dimensional conformal field theories
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Entanglement hamiltonian evolution during thermalization in conformal field theory
• Operator content of entanglement spectra after global quenches in the transverse field Ising chain
• Decoherence in Conformal Field Theory
• Late Time Quantum Chaos of pure states in the SYK model
• Rényi Mutual Information for Free Scalar in Even Dimensions
• About the quantum Talbot effect on the sphere
• Quantum revivals in free field CFT