Evolutions of entanglement and complexity after a thermal quench in massive gravity theory

Abstract

We study the evolution of the holographic entanglement entropy (HEE) and the holographic complexity (HC) after a thermal quench in 1 + 1 dimensional boundary CFTs dual to massive BTZ black holes. The study indicates how the graviton mass m g , the charge q, and also the size of the boundary region l determine the evolution of the HEE and HC. We find that for small q and l, the evolutions of the HEE and the HC is a continuous function. When q or l is tuned larger, the discontinuity emerges, which could not observed in the neutral AdS 3 backgrounds. We show that, the emergence of this discontinuity is a universal behavior in the charged massive BTZ theory. With the increase of graviton mass, on the other hand, no emergence of the discontinuity behavior for any small q and l could be observed. We also show that the evolution of the HEE and HC both become stable at later times, and m g speeds up reaching to the stability during the evolution of the system. Moreover, we show that m g decreases the final stable value of HEE but raises the stable value of HC. Additionally, contrary to the usual picture in the literature that the evolution of HC has only one peak, for big enough widths, we show that graviton mass could introduce two peaks during the evolution. However, for large enough charges the one peak behavior will be recovered again. We also examine the evolutions of HEE and HC growths at the early stage, which an almost linear behavior has been detected. * Electronic address: constaantine@163.com

The connection between holographic entanglement and complexity of purification

“…Also, the same studies could be done for other geometries such as confining backgrounds [75], or Lifshitz or Hyperscaling backgrounds [76] and then study the effect of various characteristics of each of these geometries on EoP and CoP, [76,77].…”

Time dependence of complexity for Lovelock black holes

“…In the AdS/CFT correspondence, there are two popular proposals for complexity, usually dubbed by "Complexity=Volume" (CV) duality [7,8] and "Complex-ity=Action" (CA) duality [9,10]. The two conjectures have been extensively studied in literature [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]. However, there are some drawbacks for the two proposals as well.…”

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

“…In [63], the connection between entanglement of purification (EoP) and complexity of purification (CoP) has been studied. These studies could also be done for the case warped conformal field theories and check how the lack of dilation in one direction could change the EoP and CoP and their evolutions [62].…”

“…In the NMG action, the mass of graviton plays the essential role which affects various quantum information quantities of the model, such as entanglement and its evolutions during quench processes, entanglement and complexity of purification, etc, which were studied in more details in [24,37,62,63].…”