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We study holographic models related to global quantum quenches in finite size systems. The holographic set up describes naturally a CFT, which we consider on a circle and a sphere. The enhanced symmetry of the conformal group on the circle motivates us to compare the evolution in both cases. Depending on the initial conditions, the dual geometry exhibits oscillations that we holographically interpret as revivals of the initial field theory state. On the sphere, this only happens when the energy density created by the quench is small compared to the system size. However on the circle considerably larger energy densities are compatible with revivals. Two different timescales emerge in this latter case. A collapse time, when the system appears to have dephased, and the revival time, when after rephasing the initial state is partially recovered. The ratio of these two times depends upon the initial conditions in a similar way to what is observed in some experimental setups exhibiting collapse and revivals.
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Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT$_3$. We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension $Delta$ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large $Delta$ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT$_2$ case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.
In this paper, we study how quantum correlation between subsystems changes in time by investigating time evolution of mutual information and logarithmic negativity in two protocols of mass quench. Hamiltonian in both protocols is for 2-dimensional free scalar theory with time-dependent mass: the mass in one case decreases monotonically and vanishes asymptotically (ECP), and that in the other decreases monotonically before t = 0, but increases monotonically afterward, and becomes constant asymptotically (CCP). We study the time evolution of the quantum correlations under those protocols in two different limits of the mass quench; fast limit and slow limit depending on the speed with which the mass is changed. We obtain the following two results: (1) For the ECP, we find that the time evolution of logarithmic negativity is, when the distance between the two subsystems is large enough, well-interpreted in terms of the propagation of relativistic particles created at a time determined by the limit of the quench we take. On the other hand, the evolution of mutual information in the ECP depends not only on the relativistic particles but also on slowly-moving particles. (2) For the CCP, both logarithmic negativity and mutual information oscillate in time after the quench. When the subsystems are well-separated, the oscillation of the quantum correlations in the fast limit is suppressed, and the time evolution looks similar to that under the ECP in the fast limit.
Ground states of interacting QFTs are non-gaussian states, i.e. their connected n-point correlation functions do not vanish for n>2, in contrast to the free QFT case. We show that when the ground state of an interacting QFT evolves under a free massive QFT for a long time (a scenario that can be realised by a Quantum Quench), the connected correlation functions decay and all local physical observables equilibrate to values that are given by a gaussian density matrix that keeps memory only of the two-point initial correlation function. The argument hinges upon the fundamental physical principle of cluster decomposition, which is valid for the ground state of a general QFT. An analogous result was already known to be valid in the case of d=1 spatial dimensions, where it is a special case of the so-called Generalised Gibbs Ensemble (GGE) hypothesis, and we now generalise it to higher dimensions. Moreover in the case of massless free evolution, despite the fact that the evolution may not lead to equilibration but unbounded increase of correlations with time instead, the GGE gives correctly the leading order asymptotic behaviour of correlation functions in the thermodynamic and large time limit. The demonstration is performed in the context of bosonic relativistic QFT, but the arguments apply more generally.
In order to holographically model quenches with a gapped final hamiltonian, we consider a gravity-scalar theory in anti-de Sitter space with an infrared hard wall. We allow a time dependent profile for the scalar field at the wall. This induces an energy exchange between bulk and wall and generates an oscillating scalar pulse. We argue that such backgrounds are the counterpart of quantum revivals in the dual field theory. We perform a qualitative comparison with the quench dynamics of the massive Schwinger model, which has been recently analyzed using tensor network techniques. Agreement is found provided the width of the oscillating scalar pulse is inversely linked to the energy density communicated by the quench. We propose this to be a general feature of holographic quenches.
We study overlaps between two regularized boundary states in conformal field theories. Regularized boundary states are dual to end of the world branes in an AdS black hole via the AdS/BCFT. Thus they can be regarded as microstates of a single sided black hole. Owing to the open-closed duality, such an overlap between two different regularized boundary states is exponentially suppressed as $langle psi_{a} | psi_{b} rangle sim e^{-O(h^{(min)}_{ab})}$, where $h^{(min)}_{ab}$ is the lowest energy of open strings which connect two different boundaries $a$ and $b$. Our gravity dual analysis leads to $h^{(min)}_{ab} = c/24$ for a pure AdS$_3$ gravity. This shows that a holographic boundary state is a random vector among all left-right symmetric states, whose number is given by a square root of the number of all black hole microstates. We also perform a similar computation in higher dimensions, and find that $h^{( min)}_{ab}$ depends on the tensions of the branes. In our analysis of holographic boundary states, the off diagonal elements of the inner products can be computed directly from on-shell gravity actions, as opposed to earlier calculations of inner products of microstates in two dimensional gravity.
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