Abstract We investigate the behavior of the return amplitude ( t ) = ∣ 〈 Ψ ( 0 ) ∣ Ψ ( 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 ∣ Ψ ( 0 ) 〉 of extensive energy with short-range correlations. After an initial gaussian decay ( 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 ( σ 1 / ( d − 1 ) L ) , where σ ≫ 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 ∼ integer × L . In particular, on a sphere S d − 1 of circumference 2 π L , there is an action of the modular group on ( t ) implying structure near all rational values of t / L , similar to what happens for rational CFTs in d = 2 .
We consider a quantum quench in a finite system of length
L described by a
1+1-dimensional conformal field theory (CFT), of central charge
c, from a state with finite energy density corresponding to an inverse temperature $\ensuremath{\beta}\ensuremath{\ll}L$. For times
t such that $\ensuremath{\ell}/2<t<(L\ensuremath{-}\ensuremath{\ell})/2$ the reduced density matrix of a subsystem of length $\ensuremath{\ell}$ is exponentially close to a thermal density matrix. We compute exactly the overlap
F of the state at time
t with the initial state and show that in general it is exponentially suppressed at large $L/\ensuremath{\beta}$. However, for minimal models with
c<1 (more generally, rational CFTs), at times which are integer multiples of
L/2 (for periodic boundary conditions,
L for open boundary conditions) there are (in general, partial) revivals at which
F is
O(1), leading to an eventual complete revival with
F=1. There is also interesting structure at all rational values of
t/L, related to properties of the CFT under modular transformations. At early times $t\ensuremath{\ll}(L\ensuremath{\beta}{)}^{1/2}$ there is a universal decay $\mathcal{F}\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}(\ensuremath{\pi}c/3)L{t}^{2}/\ensuremath{\beta}({\ensuremath{\beta}}^{2}+4{t}^{2}))$. The effect of an irrelevant nonintegrable perturbation of the CFT is to progressively broaden each revival at
t=nL/2 by an amount
O(n1/2).
A bstract In this paper, we look for signatures of quantum revivals in two-dimensional conformal field theories (2d CFTs) on a spatially compact manifold by using operator entanglement. It is believed that thermalization does not occur on spatially compact manifolds as the quantum state returns to its initial state which is a phenomenon known as quantum revival. We find that in CFTs such as the free fermion CFT, the operator mutual information exhibits quantum revival in accordance with the relativistic propagation of quasiparticles while in holographic CFTs, the operator mutual information does not exhibit this revival and the quasiparticle picture breaks down. Furthermore, by computing the tripartite operator mutual information, we find that the information scrambling ability of holographic CFTs can be weakened by the finite size effect. We propose a modification of an effective model known as the line tension picture to explain the entanglement dynamics due to the strong scrambling effect and find a close relationship between this model and the wormhole (Einstein-Rosen Bridge) in the holographic bulk dual.
Abstract The recent work by Cardy (arXiv: 1603.08267 ) on quantum revivals and higher dimensional CFT is revisited and enlarged upon for free fields. The expressions for the free energy used here are those derived some time ago. The calculation is extended to spin–half fields for which the power spectrum involves the odd divisor function. An explanation of the rational revivals for odd spheres is given in terms of wrongly quantised fields and modular transformations. Comments are made on the equivalence of operator counting and eigenvalue methods, which is quickly verified.
Abstract. We describe several results concerning global quantum quenches from states with short-range correlations to quantum critical points whose low-energy properties are described by a 1 + 1-dimensional conformal field theory (CFT), extending the work of Calabrese and Cardy (2006 Phys. Rev. Lett . 96 136801 ): (a) for the special class of initial states discussed in that paper we show that, once a finite region falls inside the horizon, its reduced density matrix is exponentially close in L 2 norm to that of a thermal Gibbs state; (b) small deformations of this initial state in general lead to a (non-Abelian) generalized Gibbs distribution with, however, the possibility of parafermionic conserved charges; (c) small deformations of the CFT, corresponding to curvature of the dispersion relation and (non-integrable) left-right scattering, lead to a dependence of the speed of propagation on the initial state, as well as diffusive broadening of the horizon.
We study the time evolution of single interval Rényi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width ϵ. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order ϵ2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ϵ2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ϵ2 correction to the entanglement entropy for small μ, and show that the contribution at order μ 2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.
Abstract In this paper, we initiate the study of operator local quenches in non-conformal field theories. We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension and generalize the well-known two-dimensional CFT results. We derive the energy density, U(1)-charge density and ϕ2(x)-condensate post-quench dynamics, and identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. For local quenches in higher-dimensional free massless scalar theories, we reproduce the structure of the available holographic results. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables with a complicated localization/delocalization pattern.