Linear growth of entanglement entropy in holographic thermalization captured by horizon interiors and mutual information

Abstract

We study the holographic entanglement entropy in a homogeneous falling shell background, which is dual to the strongly coupled field theory following a global quench. For d=2 conformal field theories, it is known that the entropy has a linear growth regime if the scale of the entangling region is large. In addition, the growth rate approaches a constant when the scale increases. We demonstrate analytically that this behavior is directly related to the part of minimal area surface probing the interior of apparent horizons in the bulk, as well as the mutual information between two disjoint rectangular subsystems in the boundary. Furthermore, we show numerically that all the results are universal for the d=3 conformal field theory, the non-relativistic scale-invariant theory and the dual theory of Gauss-Bonnet gravity.

Time evolution of entanglement for holographic steady state formation

“…For example, in [8-14, 16, 50] it was found that after a global quench, an initial quadratic growth of entanglement with time is followed by a universal linear growth regime. The special case where the final state is an AdS-Schwarzschild black hole is referred to as entanglement tsunami [12][13][14]. Noteworthy, in [14] the linear growth is found to be independent of the choice of entangling regions.…”

“…Then, these solutions are refined by using Newton's method that yields the solution with the desired accuracy, in our case fifteen digits. If more than one solution is regular in the sense that the length is positive, the final answer is taken to 13 Even upon expressing hyperbolic functions in terms of exponentials and changing variable from x to ξ = exp(Ax), the exponents of new the variable are non-integer for any choice of A.…”

“…For example, in a series of papers [8][9][10][11][12][13][14]50], 16 it was found that after a global quench, the entanglement entropy of a sufficiently large boundary region would exhibit an initial quadratic growth of entanglement with time,…”

Aspects of holographic entanglement at finite temperature and chemical potential

“…Mutual information has several advantages over entanglement entropy. In the context of holography, mutual information has been used extensively to study various aspects of quantum entanglement, for example see [8,[25][26][27][28][44][45][46][47][48][49].…”

Thermalization of mutual information in hyperscaling violating backgrounds

“…The corresponding metric is given by (1.4). For example entanglement entropy has been studied in [23][24][25][26][27][28][29][30][31][32] and mutual information in [33][34][35][36]. Now it is natural to study the time-dependency of the holographic entanglement entropy and mutual information in time-dependent hyperscaling violating background.…”