Holographic subregion complexity under a thermal quench

Abstract

We study the evolution of holographic subregion complexity under a thermal quench in this paper. From the subregion CV proposal in the AdS/CFT correspondence, the subregion complexity in the CFT is holographically captured by the volume of the codimension-one surface enclosed by the codimension-two extremal entanglement surface and the boundary subregion. Under a thermal quench, the dual gravitational configuration is described by a Vaidya-AdS spacetime. In this case we find that the holographic subregion complexity always increases at early time, and after reaching a maximum it decreases and gets to saturation. Moreover we notice that when the size of the strip is large enough and the quench is fast enough, in $AdS_{d+1}(d\geq3)$ spacetime the evolution of the complexity is discontinuous and there is a sudden drop due to the transition of the extremal entanglement surface. We discuss the effects of the quench speed, the strip size, the black hole mass and the spacetime dimension on the evolution of the subregion complexity in detail numerically.

Figures (13)

• Figure 1: The profile of the minimal surface of an infinite strip in pure $AdS$ background.
• Figure 2: The evolution of holographic entanglement entropy with respect to the boundary time $t$. We fix $M=1$ and $v_{0}=0.01$ here. The transition point in the right panel locates at $t=3.3248,\hat{S}=1.7437$.
• Figure 3: The evolution of $z_{\ast}$ with respect to boundary time $t$. We fix $M=1$ and $v_{0}=0.01$ here. The orange parts correspond to the surfaces of the minimum area. The transition point locates at $t=3.3248$ in the right panel.
• Figure 4: The evolution of extremal surface $\gamma_{\mathcal{A}}=(\tilde{z}(x),\tilde{v}(x))$ for $AdS_{3}$ and $l=2$. We fix $M=1$ and $v_{0}=0.01$ here. The left panel shows the evolution in $(x,v,z)$. The right panel shows their projection on to the $(x,z)$ plane. The extremal surface evolves from left to right in the left panel and from up to down in the right panel.
• Figure 5: The evolution of extremal surface $\gamma_{\mathcal{A}}=(\tilde{z}(x),\tilde{v}(x))$ for $AdS_{4}$ and $l=5$. We fix $M=1$ and $v_{0}=0.01$ here.