Scrambling of Entanglement from Integrability to Chaos: Bootstrapped Time-Integrated Spread Complexity

Abstract

A physical relationship for the combination of scrambling via spread complexity and entanglement is characterized by the fidelity of quantum unitary dynamics. Time-integrated quantities for the degree of quantum ergodicity capture state spreading from initial to late times under physically plausible operator perturbations. Selecting maximally entangled state as a initial condition evaluates the scrambling of entanglement in this setting. For this reason, we utilize the Rosenzweig-Porter ensembles across different ergodic regimes. Computed integrated spread complexity and associated integrated quantum state fidelity display a monotonic inverse relationship for maximally entangled states from integrability to chaos. Information bounds in non-local high-energy systems and holographic scrambling can be evaluated with this approach.

16 pages, 4 figures, 96 citations. This version: JHEP format, improvements in text and formulation, n+1 weighting, data regeneration and re-plots after n+1. Dataset is available on zenodo https://zenodo.org/records/19707590 and leymosun package v0.4.32 is used https://github.com/msuzen/leymosun