Moment method and continued fraction expansion in Floquet Operator Krylov Space

• URL: http://arxiv.org/abs/2410.15223v1
• Date: Sat, 19 Oct 2024 21:59:29 GMT
• Title: Moment method and continued fraction expansion in Floquet Operator Krylov Space
• Authors: Hsiu-Chung Yeh, Aditi Mitra,
• Abstract summary: Recursion methods map complex dynamics to an effective non-interacting problem in one dimension. We present an application of this showing that a moment method exists where given an autocorrelation function, one can construct the corresponding Krylov angles. We highlight certain special cases: stable $m$-periodic dynamics derived using the method of continued fractions, exponentially decaying and power-law decaying stroboscopic dynamics.
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• 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 $m$-periodic dynamics derived using the method of continued fractions, exponentially decaying and power-law decaying stroboscopic dynamics. Remarkably, our examples of stable $m$-periodic dynamics correspond to $m$-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.

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