Floquet Schrieffer-Wolff transform based on Sylvester equations

• URL: http://arxiv.org/abs/2407.08405v2
• Date: Fri, 13 Sep 2024 20:51:11 GMT
• Title: Floquet Schrieffer-Wolff transform based on Sylvester equations
• Authors: Xiao Wang, Fabio Pablo Miguel Méndez-Córdoba, Dieter Jaksch, Frank Schlawin,
• Abstract summary: We show how to solve Sylvester equations without knowledge of the eigenstates of the undriven many-body system. In the limit of high driving frequencies, these solutions reduce to the well-known high-frequency limit of the Floquet-Magnus expansion.
• Score: 4.58527340094927
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a Floquet Schrieffer Wolff transform (FSWT) to obtain effective Floquet Hamiltonians and micro-motion operators of periodically driven many-body systems for any non-resonant driving frequency. The FSWT perturbatively eliminates the oscillatory components in the driven Hamiltonian by solving operator-valued Sylvester equations. We show how to solve these Sylvester equations without knowledge of the eigenstates of the undriven many-body system, using the driven Hubbard model as an example. In the limit of high driving frequencies, these solutions reduce to the well-known high-frequency limit of the Floquet-Magnus expansion. We anticipate this method will be useful for describing multi-orbital and long-range interacting systems driven in-gap.

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