Abstract
We investigate general features of the evolution of holographic subregion complexity (HSC) on Vaidya-AdS metric with a general form. The spacetime is dual to a sudden quench process in quantum system and HSC is a measure of the “difference” between two mixed states. Based on the subregion CV (Complexity equals Volume) conjecture and in the large size limit, we extract out three distinct stages during the evolution of HSC: the stage of linear growth at the early time, the stage of linear growth with a slightly small rate during the intermediate time and the stage of linear decrease at the late time. The growth rates of the first two stages are compared with the Lloyd bound. We find that with some choices of certain parameter, the Lloyd bound is always saturated at the early time, while at the intermediate stage, the growth rate is always less than the Lloyd bound. Moreover, the fact that the behavior of CV conjecture and its version of the subregion in Vaidya spacetime implies that they are different even in the large size limit.
Highlights
An intriguing topic is to investigate the evolution behavior of holographic subregion complexity (HSC) during a holographic quench process, which may be described by the Vaidya-AdS spacetime [29, 30]
We find that with some choices of certain parameter, the Lloyd bound is always saturated at the early time, while at the intermediate stage, the growth rate is always less than the Lloyd bound
At the very early time right after the null shell begins to fall down, the HSC grows with a linear manner no matter the size of the subregion is
Summary
We will firstly introduce the general Vaidya metric in the form of EddingtonFinkelstein coordinates. For a strip boundary region A, we will obtain some solutions for the corresponding HRT surface which are crucial for the derivation of the HSC. After that we turn to describe the configuration of critical HRT surfaces which is essential for us to understand the behavior of HSC during the intermediate stage of the evolution. In the end of this section, we will derive the expression of HSC
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