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

TL;DR

This paper introduces a time-integrated measure to analyze quantum ergodicity and entanglement scrambling, demonstrating its effectiveness across different regimes using numerical ensembles.

Contribution

It proposes a novel, numerically bootstrapped measure for diagnosing quantum ergodicity and entanglement scrambling, bridging the gap between spread complexity and fidelity decay.

Findings

Integrated spread complexity varies monotonically with ergodic regimes.

The measure provides fine-grained resolution across different ergodic behaviors.

It offers a complementary tool for diagnosing quantum scrambling and ergodicity.

Abstract

A time-integrated measure of spread complexity and fidelity are proposed to diagnose the degree of quantum ergodicity and the behavior of scrambling of entanglement simultaneously. We quantify the scrambling dynamics of maximally entangled states by employing numerically bootstrapped realizations from an ensemble of Hamiltonians, where we show that this is mathematically equivalent to perturbing unitary evolutions. Using Rosenzweig-Porter ensembles, we show that the integrated spread complexity provides a fine-grained resolution across different ergodic regimes, exhibiting a monotonic inverse relationship with the decay of integrated fidelity for maximally entangled states. This approach offers a complementary diagnosis for quantum ergodicity for scrambling of entanglement.