Flow Equation Approach to Periodically Driven Quantum Systems

被引:55
作者
Vogl, Michael [1 ]
Laurell, Pontus [1 ]
Barr, Aaron D. [1 ]
Fiete, Gregory A. [1 ,2 ,3 ]
机构
[1] Univ Texas Austin, Dept Phys, Austin, TX 78712 USA
[2] Northeastern Univ, Dept Phys, Boston, MA 02115 USA
[3] MIT, Dept Phys, Cambridge, MA 02139 USA
来源
PHYSICAL REVIEW X | 2019年 / 9卷 / 02期
关键词
ULTRAFAST; DYNAMICS; STATES; CHAIN;
D O I
10.1103/PhysRevX.9.021037
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization-group-like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency-and drive strength-regimes that are usually inaccessible via high-frequency omega expansions in the parameter h/omega, where h is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy model and test an approximate version of it on both interacting and noninteracting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high-frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high-frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel nonequilibrium regimes and behaviors in driven quantum many-particle systems.
引用
收藏
页数:25
相关论文
共 102 条
  • [31] Observation of dynamical vortices after quenches in a system with topology
    Flaeschner, N.
    Vogel, D.
    Tarnowski, M.
    Rem, B. S.
    Luehmann, D. -S.
    Heyl, M.
    Budich, J. C.
    Mathey, L.
    Sengstock, K.
    Weitenberg, C.
    [J]. NATURE PHYSICS, 2018, 14 (03) : 265 - +
  • [32] Emergent ultrafast phenomena in correlated oxides and heterostructures
    Gandolfi, M.
    Celardo, G. L.
    Borgonovi, F.
    Ferrini, G.
    Avella, A.
    Banfi, F.
    Giannetti, C.
    [J]. PHYSICA SCRIPTA, 2017, 92 (03)
  • [33] Gerasimenko Ya. A., ARXIV170408149
  • [34] Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach
    Giannetti, Claudio
    Capone, Massimo
    Fausti, Daniele
    Fabrizio, Michele
    Parmigiani, Fulvio
    Mihailovic, Dragan
    [J]. ADVANCES IN PHYSICS, 2016, 65 (02) : 58 - 238
  • [35] Periodically driven quantum matter: The case of resonant modulations
    Goldman, N.
    Dalibard, J.
    Aidelsburger, M.
    Cooper, N. R.
    [J]. PHYSICAL REVIEW A, 2015, 91 (03):
  • [36] Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields
    Goldman, N.
    Dalibard, J.
    [J]. PHYSICAL REVIEW X, 2014, 4 (03):
  • [37] Floquet Spectrum and Transport through an Irradiated Graphene Ribbon
    Gu, Zhenghao
    Fertig, H. A.
    Arovas, Daniel P.
    Auerbach, Assa
    [J]. PHYSICAL REVIEW LETTERS, 2011, 107 (21)
  • [38] SPONTANEOUS DIMERIZATION IN THE S=1/2 HEISENBERG ANTI-FERROMAGNETIC CHAIN WITH COMPETING INTERACTIONS
    HALDANE, FDM
    [J]. PHYSICAL REVIEW B, 1982, 25 (07): : 4925 - 4928
  • [39] Onset of Floquet thermalization
    Haldar, Asmi
    Moessner, Roderich
    Das, Arnab
    [J]. PHYSICAL REVIEW B, 2018, 97 (24)
  • [40] Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model
    Heyl, M.
    Polkovnikov, A.
    Kehrein, S.
    [J]. PHYSICAL REVIEW LETTERS, 2013, 110 (13)