Moment method and continued fraction expansion in Floquet Operator Krylov Space
Abstract
Recursion methods such as Krylov techniques map complex dynamics to an effective non-interacting problem in one dimension. For example, the operator Krylov space for Floquet dynamics can be mapped to the dynamics of an edge operator of the one-dimensional Floquet inhomogeneous transverse field Ising model (ITFIM), where the latter, after a Jordan-Wigner transformation, is a Floquet model of non-interacting Majorana fermions, and the couplings correspond to Krylov angles. We present an application of this showing that a moment method exists where given an autocorrelation function, one can construct the corresponding Krylov angles, and from that the corresponding Floquet-ITFIM. Consequently, when no solutions for the Krylov angles are obtained, it indicates that the autocorrelation is not generated by unitary dynamics. We highlight this by studying certain special cases: stable -periodic dynamics derived using the method of continued fractions, exponentially decaying and power-law decaying stroboscopic dynamics. Remarkably, our examples of stable -periodic dynamics correspond to -period edge modes for the Floquet-ITFIM where deep in the chain, the couplings correspond to a critical phase. Our results pave the way to engineer Floquet systems with desired properties of edge modes and also provide examples of persistent edge modes in gapless Floquet systems.
Keywords
Cite
@article{arxiv.2410.15223,
title = {Moment method and continued fraction expansion in Floquet Operator Krylov Space},
author = {Hsiu-Chung Yeh and Aditi Mitra},
journal= {arXiv preprint arXiv:2410.15223},
year = {2025}
}