Heating and many-body resonances in a periodically driven two-band system

We study the dynamics and stability in a strongly interacting resonantly driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the time evolution is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is relatively fast in these two regimes (but to different “temperatures”), in the crossover between them we find slow nonthermalizing time evolution: temporal fluctuations become strong and temporal correlations long lived. Microscopically, we trace back the origin of this nonthermalizing time evolution to the properties of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the approximate energy conservation, and thus produces thermalization to infinite temperature.We thank D. Abanin, Ye. Bar Lev, I. Bloch, L. D'Alessio, M. Dolfi, S. Gopalakrishnan, T. Grover, V. Khemani, M. Kolodrubetz, A. Lazarides, U. Schneider, and C. Weitenberg for insightful and interesting discussions, and especially acknowledge the help of P. Weinberg for co-developing the exact diagonalization code used in this work. D.H. is the Addie and Harold Broitman Member at I. A. S. This work was supported by AFOSR FA9550-13-1-0039, NSF DMR-1506340, ARO W911NF1410540, and the Deutsche Akademie der Naturforscher Leopoldina (Grants No. LPDS 2013-07 and No. LPDR 2015-01). The computational work reported on in this paper was partly performed on the Shared Computing Cluster which is administered by Boston University's Research Computing Services (www.bu.edu/tech/support/research). The authors also acknowledge the Research Computing Services group for providing consulting support. (FA9550-13-1-0039 - AFOSR; DMR-1506340 - NSF; W911NF1410540 - ARO; LPDS 2013-07 - Deutsche Akademie der Naturforscher Leopoldina; LPDR 2015-01 - Deutsche Akademie der Naturforscher Leopoldina)Accepted manuscrip