Exploring quantum ergodicity of unitary evolution through the Krylov approach
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.
Cite
@article{arxiv.2407.06428,
title = {Exploring quantum ergodicity of unitary evolution through the Krylov approach},
author = {Gastón F. Scialchi and Augusto J. Roncaglia and Carlos Pineda and Diego A. Wisniacki},
journal= {arXiv preprint arXiv:2407.06428},
year = {2025}
}
Comments
10 pages, 7 figures. v2: updated to match published version