Entanglement features of random Hamiltonian dynamics

We introduce the concept of entanglement features of unitary gates, as a collection of exponentiated entanglement entropies over all bipartitions of input and output channels. We obtained the general formula for time-dependent nth-R\'enyi entanglement features for unitary gates generated by random Hamiltonian. In particular, we propose an Ising formulation for the second R\'enyi entanglement features of random Hamiltonian dynamics, which admits a holographic tensor network interpretation. As a general description of entanglement properties, we show that the entanglement features can be applied to several dynamical measures of thermalization, including the out-of-time-order correlation and the entanglement growth after a quantum quench. We also analyze the Yoshida-Kitaev probabilistic protocol for random Hamiltonian dynamics.