Geometric Floquet Theory
We derive Floquet theory from quantum geometry. We identify quasienergy folding as a consequence of a broken gauge group of the adiabatic gauge potential U(1)↦Z. Fixing instead the gauge freedom using the parallel-transport gauge uniquely decomposes Floquet dynamics into a purely geometric and a pur...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-08-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/7l91-gw77 |
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| _version_ | 1849396423146078208 |
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| author | Paul M. Schindler Marin Bukov |
| author_facet | Paul M. Schindler Marin Bukov |
| author_sort | Paul M. Schindler |
| collection | DOAJ |
| description | We derive Floquet theory from quantum geometry. We identify quasienergy folding as a consequence of a broken gauge group of the adiabatic gauge potential U(1)↦Z. Fixing instead the gauge freedom using the parallel-transport gauge uniquely decomposes Floquet dynamics into a purely geometric and a purely dynamical evolution. The dynamical average-energy operator provides an unambiguous sorting of the quasienergy spectrum, identifying a Floquet ground state and suggesting a way to define the filling of Floquet-Bloch bands. We exemplify the features of geometric Floquet theory using an exactly solvable XY model and a nonintegrable kicked Ising chain. We elucidate the geometric origin of inherently nonequilibrium effects, like the π-quasienergy splitting in discrete time crystals or π-edge modes in anomalous Floquet topological insulators. The spectrum of the average-energy operator is a susceptible indicator for both heating and spatiotemporal symmetry-breaking transitions. Last, we demonstrate that the periodic lab-frame Hamiltonian generates transitionless counterdiabatic driving for Floquet eigenstates. This work directly bridges seemingly unrelated areas of nonequilibrium physics. |
| format | Article |
| id | doaj-art-593414e5ca7a43aaadfdb4497d41504a |
| institution | Kabale University |
| issn | 2160-3308 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj-art-593414e5ca7a43aaadfdb4497d41504a2025-08-20T03:39:21ZengAmerican Physical SocietyPhysical Review X2160-33082025-08-0115303103710.1103/7l91-gw77Geometric Floquet TheoryPaul M. SchindlerMarin BukovWe derive Floquet theory from quantum geometry. We identify quasienergy folding as a consequence of a broken gauge group of the adiabatic gauge potential U(1)↦Z. Fixing instead the gauge freedom using the parallel-transport gauge uniquely decomposes Floquet dynamics into a purely geometric and a purely dynamical evolution. The dynamical average-energy operator provides an unambiguous sorting of the quasienergy spectrum, identifying a Floquet ground state and suggesting a way to define the filling of Floquet-Bloch bands. We exemplify the features of geometric Floquet theory using an exactly solvable XY model and a nonintegrable kicked Ising chain. We elucidate the geometric origin of inherently nonequilibrium effects, like the π-quasienergy splitting in discrete time crystals or π-edge modes in anomalous Floquet topological insulators. The spectrum of the average-energy operator is a susceptible indicator for both heating and spatiotemporal symmetry-breaking transitions. Last, we demonstrate that the periodic lab-frame Hamiltonian generates transitionless counterdiabatic driving for Floquet eigenstates. This work directly bridges seemingly unrelated areas of nonequilibrium physics.http://doi.org/10.1103/7l91-gw77 |
| spellingShingle | Paul M. Schindler Marin Bukov Geometric Floquet Theory Physical Review X |
| title | Geometric Floquet Theory |
| title_full | Geometric Floquet Theory |
| title_fullStr | Geometric Floquet Theory |
| title_full_unstemmed | Geometric Floquet Theory |
| title_short | Geometric Floquet Theory |
| title_sort | geometric floquet theory |
| url | http://doi.org/10.1103/7l91-gw77 |
| work_keys_str_mv | AT paulmschindler geometricfloquettheory AT marinbukov geometricfloquettheory |