Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems

By D. Abanin, Wojciech De Roeck, Wen Wei Ho, F. Huveneers. 2015

305 citations recorded by the source corpus.

We establish some general dynamical properties of quantum many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasiconserved extensive quantity ${H}_{*}$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well approximated by the evolution with the Hamiltonian ${H}_{*}$ up to time ${\ensuremath{\tau}}_{*}$, which is exponentially large in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where ${H}_{*}$ is ergodic, the driven system prethermalizes to a thermal state described by ${H}_{*}$ at intermediate times $t\ensuremath{\lesssim}{\ensuremath{\tau}}_{*}$, eventually heating up to an infinite-temperature state after times $t\ensuremath{\sim}{\ensuremath{\tau}}_{*}$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a84e05d82aa0edd94d302b97a754f9cc4ca137b8

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

In Statistical and Nonlinear Physics

Citations in the corpus

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems (2015, background): “However, in dimension 1, we can obtain e , see [1], at the cost of restricting H to be a sum of strictly local terms.”
Pre-thermal phases of matter protected by time-translation symmetry (2016, methodology): “[74], who consider the supremum over t rather than the average.”
Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, background): “In this limit rigorous results for slow heating were recently established (Abanin, De Roeck, and Huveneers, 2015; Kuwahara, Mori, and Saito, 2016; Mori, Kuwahara, and Saito, 2016; Abanin et al., 2017a, 2017b; Ho, Protopopov, and Abanin, 2018; Mori et al., 2018).”
Prethermalization and Thermalization in Isolated Quantum Systems (2018, background): “In general, they quickly reach a time-periodic state that can be identified as a Gibbs state corresponding to an effective Hamiltonian, before relaxing to the thermal (infinite-temperature [26, 27]) state in a timescale that is exponentially long in the frequency of the drive [28–33].”