Periodically driven ergodic and many-body localized quantum systems

By P. Ponte, Anushya Chandran, Z. Papi'c, D. Abanin. 2014

319 citations recorded by the source corpus.

We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.

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

View Paper: https://www.semanticscholar.org/paper/2fb3e31e4c3b869dfc89d629318e1ceb60a7609f

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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. V. Khemani
2. A. Nahum
3. Matthew Fisher
4. D. Abanin
5. Maksym Serbyn
6. S. Vijay
7. I. Bloch
8. E. Altman

In Statistical and Nonlinear Physics

1. V. Khemani
2. A. Nahum
3. Maksym Serbyn
4. I. Bloch
5. Matthew Fisher
6. D. Abanin
7. S. Vijay
8. Wojciech De Roeck

Citations in the corpus

• Colloquium : Many-body localization, thermalization, and entanglement (2018, background): “(D’Alessio and Rigol, 2014; Lazarides et al., 2014; Ponte et al., 2015b), which argued that ergodic systems satisfying ETH heat up indefinitely under driving.”
• 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.”
• Integrals of motion in the many-body localized phase (2014, unknown): “tems(e.g. periodicallydrivensystems)thathavenoconservedlocaldensities andthusnomeaningfuld.c.transport,oneshoulddefineMBLmoregenerallyasaphase whereanylocalobservabledoesnotthermalizewithprobabilityone[5,6]. 3Quantummechanicsprovidesquitetriviallyalargesetofmutuallycommuting,conservedoperatorsinanysy”