Floquet systems with continuous dynamical symmetries: characterization, time-dependent Noether charge, and solvability
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| Format: | Preprint |
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2023
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| _version_ | 1866913434585530368 |
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| author | Kaneko, Yukio Ikeda, Tatsuhiko N. |
| author_facet | Kaneko, Yukio Ikeda, Tatsuhiko N. |
| contents | We study quantum Floquet (periodically-driven) systems having continuous dynamical symmetry (CDS) consisting of a time translation and a unitary transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly constrains the possible Hamiltonians $H(t)$ and allows us to obtain all the Floquet states by solving a finite-dimensional eigenvalue problem. Besides, Noether's theorem leads to a time-dependent conservation charge, whose expectation value is time-independent throughout evolution. We exemplify these consequences of CDS in the seminal Rabi model, an effective model of a nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin models in rotating fields. Our results provide a systematic way of solving for Floquet states and explain how they avoid hybridization in quasienergy diagrams. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_02143 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Floquet systems with continuous dynamical symmetries: characterization, time-dependent Noether charge, and solvability Kaneko, Yukio Ikeda, Tatsuhiko N. Mesoscale and Nanoscale Physics Quantum Gases Statistical Mechanics Optics Quantum Physics We study quantum Floquet (periodically-driven) systems having continuous dynamical symmetry (CDS) consisting of a time translation and a unitary transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly constrains the possible Hamiltonians $H(t)$ and allows us to obtain all the Floquet states by solving a finite-dimensional eigenvalue problem. Besides, Noether's theorem leads to a time-dependent conservation charge, whose expectation value is time-independent throughout evolution. We exemplify these consequences of CDS in the seminal Rabi model, an effective model of a nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin models in rotating fields. Our results provide a systematic way of solving for Floquet states and explain how they avoid hybridization in quasienergy diagrams. |
| title | Floquet systems with continuous dynamical symmetries: characterization, time-dependent Noether charge, and solvability |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Statistical Mechanics Optics Quantum Physics |
| url | https://arxiv.org/abs/2308.02143 |