Entanglement and chaos near critical point in strongly coupled gauge theory

Abstract

We perform a holographic study of the high and low temperature behaviours of logarithmic negativity (LN) and entanglement wedge cross section (EWCS) in a large $N$ strongly coupled thermal field theory with critical point having a well defined gravity dual known as 1RC black hole. The critical point is defined via $\xi \to 2$ limit where, $\xi$ is dimensionless parameter proportional to the charge of the 1RC black hole. We show that the logarithmic negativity in low and high thermal limits enhances with increasing $\xi$. We analytically compute the EWCS in low and high thermal limits and find an agreement with the previously reported numerical results. We holographically explore the correlation between two identical copies of thermal field theory with critical point forming a thermofield double state (TFD) by computing the thermo mutual information (TMI). TMI shows an increasing behaviour with respect to the width of the boundary region. Further, we analyze the impact of an early perturbation on the field theory by analyzing a shock wave perturbation that grows exponentially in the dual eternal 1 RC black hole and then estimate the degradation of TMI. However rate of such disruption of TMI slows down as the value of critical parameter $\xi$ takes higher values.

43 pages, 14 figures, title changed, major revision, many explanation added, accepted for publication in the European Physical Journal C (EPJC)

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