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arXiv · 2407.08405

Floquet Schrieffer-Wolff transform based on Sylvester equations

Xiao Wang·Fabio Pablo Miguel Méndez-Córdoba·Dieter Jaksch·Frank Schlawin
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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 with systematic approximations. It goes beyond various high-frequency expansion methods commonly used in Floquet theory, as we demonstrate with the example of the driven Fermi-Hubbard model. In the limit of high driving frequencies, the FSWT Hamiltonian reduces to the widely used Floquet-Magnus result. We anticipate this method will be useful for designing Rydberg multi-qubit gates, controlling correlated hopping in quantum simulations in optical lattices, and describing multi-orbital and long-range interacting systems driven in-gap.

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Xiao Wang, Fabio Pablo Miguel Méndez-Córdoba, Dieter Jaksch, Frank Schlawin. 2024-07-11. Floquet Schrieffer-Wolff transform based on Sylvester equations. https://doi.org/10.1103/physrevb.110.245108

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