Long-time Behavior of Isolated Periodically Driven Interacting Lattice Systems

We study the dynamics of isolated interacting spin chains that are periodically driven by sudden quenches. Using full exact diagonalization of finite chains, we show that these systems exhibit three distinct regimes. For short driving periods, the Floquet Hamiltonian is well approximated by the time...

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Bibliographic Details
Published inPhysical review. X Vol. 4; no. 4; p. 041048
Main Authors D’Alessio, Luca, Rigol, Marcos
Format Journal Article
LanguageEnglish
Published College Park American Physical Society 01.12.2014
Subjects
Approximation
Chains
Energy absorption
Evolution
Hamiltonian functions
High power lasers
Incident light
Operators (mathematics)
Pendulums
Room temperature
Shaking
Spin dynamics
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Summary:We study the dynamics of isolated interacting spin chains that are periodically driven by sudden quenches. Using full exact diagonalization of finite chains, we show that these systems exhibit three distinct regimes. For short driving periods, the Floquet Hamiltonian is well approximated by the time-averaged Hamiltonian, while for long periods, the evolution operator exhibits properties of random matrices of a circular ensemble (CE). In between, there is a crossover regime. Based on a finite-size scaling analysis and analytic arguments, we argue that, for thermodynamically large systems and nonvanishing driving periods, the evolution operator always exhibits properties of the CE of random matrices. Consequently, the Floquet Hamiltonian is a nonlocal Hamiltonian with multispin interaction terms, and the driving leads to the equivalent of an infinite temperature state at long times. These results are connected to the breakdown of the Magnus expansion and are expected to hold beyond the specific lattice model considered.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.4.041048