Floquet Schrieffer-Wolff transform based on Sylvester equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913663268421632 |
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| author | Wang, Xiao Méndez-Córdoba, Fabio Pablo Miguel Jaksch, Dieter Schlawin, Frank |
| author_facet | Wang, Xiao Méndez-Córdoba, Fabio Pablo Miguel Jaksch, Dieter Schlawin, Frank |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Floquet Schrieffer-Wolff transform based on Sylvester equations Wang, Xiao Méndez-Córdoba, Fabio Pablo Miguel Jaksch, Dieter Schlawin, Frank Quantum Physics Strongly Correlated Electrons 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. |
| title | Floquet Schrieffer-Wolff transform based on Sylvester equations |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2407.08405 |