Exploring quantum ergodicity of unitary evolution through the Krylov approach

TL;DR

This paper investigates the robustness of a Krylov-based approach to quantum ergodicity, demonstrating its effectiveness in detecting the transition from integrability to chaos in various quantum systems.

Contribution

It introduces a Krylov approach to quantum ergodicity applicable to both autonomous and kicked systems, extending previous methods and validating with random matrix and spin chain examples.

Findings

Krylov approach effectively detects chaos transition

Method is robust for different quantum system types

Validated with random matrix and spin chain models

Abstract

In recent years, there has been growing interest in characterizing the complexity of quantum evolutions of interacting many-body systems. When a time-independent Hamiltonian governs the dynamics, Krylov complexity has emerged as a powerful tool. For unitary evolutions like kicked systems or Trotterized dynamics, a similar formulation based on the Arnoldi approach has been proposed yielding a new notion of quantum ergodicity [P. Suchsland, R. Moessner, and P. W. Claeys, Phys. Rev. B 111, 014309 (2025)]. In this work, we show that this formulation is robust for observing the transition from integrability to chaos in both autonomous and kicked systems. Examples from random matrix theory and spin chains are shown in this paper.