Bath deformations, islands, and holographic complexity

Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of the bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the anti-de Sitter-Schwarzschild to the Kasner universe in the bulk. The subregion complexity shows a discontinuous jump at Page time at a fixed perturbation, where the discontinuity depends solely on the system's parameters. We show that the amount of discontinuity decreases with the perturbation as well as with the scaling dimension of the relevant scalar operator.