2025/06/25 by Hsiu-Chung Yeh, Yeh, Hsiu-Chung, Aditi Mitra +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2506.20611
openalex publication_date 2025/06/25 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/30
Operator spreading under stroboscopic time evolution due to a unitary is studied. An operator Krylov space is constructed and related to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parameterizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC for persistent m-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the Z3 clock model. The numerically obtained Krylov angles of the Z3 clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior.