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We study the evolution of holographic complexity of pure and mixed states in $1+1$-dimensional conformal field theory following a local quench using both the complexity equals volume (CV) and the complexity equals action (CA) conjectures. We compare the complexity evolution to the evolution of entanglement entropy and entanglement density, discuss the Lloyd computational bound and demonstrate its saturation in certain regimes. We argue that the conjectured holographic complexities exhibit some non-trivial features indicating that they capture important properties of what is expected to be effective (or physical) complexity.
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We propose a charged falling particle in an AdS space as a holographic model of local charged quench generalizing model of arXiv:1302.5703. The quench is followed by evolving currents and inhomogeneous distribution of chemical potential. We derive the analytical formula describing the evolution of the entanglement entropy. At some characteristic time after the quench, we find that the entanglement shows a sharp dip. This effect is universal and independent of the dimension of the system. At finite temperature generalization of this model, we find that multiple dips and ramps appear.
This paper is devoted to the study of the evolution of holographic complexity after a local perturbation of the system at finite temperature. We calculate the complexity using both the complexity=action(CA) and the complexity=volume(CA) conjectures and find that the CV complexity of the total state shows the unbounded late time linear growth. The CA computation shows linear growth with fast saturation to a constant value. We estimate the CV and CA complexity linear growth coefficients and show, that finite temperature leads to violation of the Lloyd bound for CA complexity. Also it is shown that for composite system after the local quench the state with minimal entanglement may correspond to the maximal complexity.
In this paper, we will propose a universal relation between the holographic complexity (dual to a volume in AdS) and the holographic entanglement entropy (dual to an area in AdS). We will explicitly demonstrate that our conjuncture hold for all a metric asymptotic to AdS$_3$, and then argue that such a relation should hold in general due to the AdS version of the Cavalieri principle. We will demonstrate that it holds for Janus solution, which have been recently been obtained in type IIB string theory. We will also show that this conjecture holds for a circular disk. This conjecture will be used to show that the proposal that the complexity equals action, and the proposal that the complexity equal volume can represent the same physics. Thus, using this conjecture, we will show that the black holes are fastest computers, using the proposal that complexity equals volume.
We investigate the evolution of complexity and entanglement following a quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger model. We demonstrate that complexity can detect quantum phase transitions and shows signatures of revivals; this observation provides a practical advantage in information processing. We also show that the complexity saturates much faster than the entanglement entropy in this system, and we provide a physical argument for this. Finally, we demonstrate that complexity is a less sensitive probe of topological order, compared with measures of entanglement.
An analytic static monopole solution is found in global AdS$_4$, in the limit of small backreaction. This solution is mapped in Poincare patch to a falling monopole configuration, which is dual to a local quench triggered by the injection of a condensate. Choosing boundary conditions which are dual to a time-independent Hamiltonian, we find the same functional form of the energy-momentum tensor as the one of a quench dual to a falling black hole. On the contrary, the details of the spread of entanglement entropy are very different from the falling black hole case where the quench induces always a higher entropy compared to the vacuum, i.e. $Delta S >0$. In the propagation of entanglement entropy for the monopole quench, there is instead a competition between a negative contribution to $Delta S$ due to the scalar condensate and a positive one carried by the freely propagating quasiparticles generated by the energy injection.
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