Effective Hamiltonians for Rapidly Driven Many-Body Lattice Systems: Induced Exchange Interactions and Density-Dependent Hoppings

Physical Review Letters
A P Itin, M I Katsnelson

Abstract

We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered,...Continue Reading

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Citations

Oct 11, 2017·Journal of Physics. Condensed Matter : an Institute of Physics Journal·J H Mentink
Jan 30, 2019·Journal of Physics. Condensed Matter : an Institute of Physics Journal·E A StepanovV V Mazurenko
Feb 13, 2016·Physical Review. E·Elena CanoviMartin Eckstein
Dec 24, 2018·Physical Review Letters·Michael MesserTilman Esslinger
Dec 31, 2016·Physical Review Letters·S RestrepoT Brandes
Apr 30, 2017·Physical Review Letters·E A StepanovM I Katsnelson
Apr 26, 2018·Physical Review Letters·D M KennesA J Millis
Aug 7, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Arnab SenK Sengupta

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