Holographic local quench and effective complexity

Abstract

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.

Holographic complexity of local quench at finite temperature

“…where we used m = 2h/L. For the limit T → 0 we reproduce the result of [17,18] where the saturation of Lloyds bound at the initial time moment τ → 0 after perturbation was found. The temperature T > 0 correction to the complexification rate at τ → 0 Figure 3.…”

“…Also this could be the drawback of the particular holographic model of local quench. Note that this model has time-reversal symmetry (also see the discussion on the related issue in [17,18]). For τ > 0 time t 1 in the formula (4.3) is given by…”

“…The local quench has a well-defined gravity dual [35] which has been investigated in the different versions further in [37]- [44]. In [17,18] we have investigated different holographic complexity proposals in the system following the local perturbation. We have considered the AdS 3 Poincare patch deformed by the static particle [35] as the background dual to the local quench.…”

Subregion complexity in holographic thermalization with dS boundary

“…While in the subregion CA proposal, complexity of subregion A is given by the on-shell gravitational action evaluated on the intersection region between WDW patch and the so-called entanglement wedge [68,69]. Also, lots of work and effort have been devoted to understand the holographic subregion complexity [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87].…”

“…For other related work, please see Refs. [83,[92][93][94][95] However, it should be noted that the boundary QFTs considered in the above mentioned work are usually living on the flat Minkowski spacetimes. It would be interesting to generalize the discussions to more realistic situations where QFTs lives on curved spacetimes, which may hep us to understand the extremely hot and condensed physics such as in the very early universe.…”