Long-time behavior of periodically driven isolated interacting lattice systems

By Luca D'Alessio, Marcos Rigol. 2014

254 citations recorded by the source corpus.

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 non-vanishing driving periods, the evolution operator always exhibits properties of CE random matrices. Consequently, the Floquet Hamiltonian is nonlocal and has multi-body interactions; 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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/c209bc586bad9e923b9fe63a348ab6d35431e14c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Michael Jason Knap
2. D. Abanin
3. I. Bloch
4. Wojciech De Roeck
5. F. Huveneers
6. U. Schneider
7. Wen Wei Ho
8. H. Lüschen

In Condensed Matter Physics

1. I. Bloch
2. U. Schneider
3. Michael Jason Knap
4. D. Abanin
5. H. Lüschen
6. P. Bordia

Citations in the corpus

• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems (2015, background): “Recent theoretical works [32, 13, 25] suggest, based on the quantum version of the ergodic hypothesis (Eigenstate Thermalization Hypothesis), that generic periodically driven many-body systems eventually do heat up to an infinite temperature, and so one would not expect the strict equality (1.”
• Periodically driving a many-body localized quantum system (2016, background): “due to the absence of level repulsion [19, 35].”