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Published on: May 30, 2014
Exploring quantum ergodicity of unitary evolution through the Krylov approach
Gastón F Scialchi1,2, Augusto J Roncaglia1,2, Carlos Pineda3
1Facultad de Ciencias Exactas y Naturales, Departamento de Física, Universidad de Buenos Aires, Buenos Aires 1428, Argentina.
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)10.1103/PhysRevB.111.014309]. 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.
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