Entanglement Features of Random Hamiltonian Dynamics

TL;DR

This paper introduces entanglement features for unitary gates generated by random Hamiltonians, providing formulas and interpretations that connect entanglement properties with thermalization measures and holographic tensor networks.

Contribution

It develops a general formula for entanglement features of random Hamiltonian dynamics and offers an Ising model formulation with holographic tensor network insights.

Findings

Derived time-dependent n-th Renyi entanglement features.

Proposed an Ising model for 2nd-Renyi entanglement features.

Linked entanglement features to thermalization measures.

Abstract

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 $n$th-Renyi entanglement features for unitary gates generated by random Hamiltonian. In particular, we propose an Ising formulation for the 2nd-Renyi 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.