Floquet perturbation theory for periodically driven weakly interacting fermions

Ghosh, Roopayan; Mukherjee, Bhaskar; Sengupta, K.

doi:10.1103/physrevb.102.235114

Cited by 26 publications

(28 citation statements)

References 69 publications

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“…First, the radius of convergence of the perturbation expansion and its regime of validity is difficult to determine. Second, the method may lead to qualitatively wrong pictures at intermediate and low drive frequencies [84]. The resolution of these issues which might provide one with a more complete picture of the FM expansion method is a long standing challenge; some progress in this direction has been made recently [50,86].…”

Section: Discussionmentioning

confidence: 99%

Analytic approaches to periodically driven closed quantum systems: methods and applications

Sen¹,

Sen²,

Sengupta³

2021

J. Phys.: Condens. Matter

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We present a brief overview of some of the analytic perturbative techniques for the computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many-body system. The key technical points about each of the methods discussed are presented in a pedagogical manner. They are followed by a brief account of some chosen phenomena where these methods have provided useful insights. We provide an extensive discussion of the Floquet-Magnus (FM) expansion, the adiabatic-impulse approximation, and the Floquet perturbation theory. This is followed by a relatively short discourse on the rotating wave approximation, a FM resummation technique and the Hamiltonian flow method. We also provide a discussion of some open problems which may possibly be addressed using these methods.

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Section: Discussionmentioning

confidence: 99%

Analytic approaches to periodically driven closed quantum systems: methods and applications

Sen¹,

Sen²,

Sengupta³

2021

J. Phys.: Condens. Matter

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“…The three colinear ordered phases given by Eqs. (35), (39) and (40) are shown in Fig. 4 (see also Ref.…”

Section: Classical Analysis and Spin-wave Theorymentioning

confidence: 96%

“…Such systems can exhibit a wide variety interesting phenomena such as dynamical freezing 2,5,8,[11][12][13][17][18][19] , the generation of non-trivial band structures and states localized at the boundaries of the system , and time crystals 31,33,86 . While periodic driving of systems of non-interacting electrons has been studied very extensively, the effects of interactions along with periodic driving have also been studied by several groups 13,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][49][50][51]85 .…”

Section: Introductionmentioning

confidence: 99%

Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term

Sur,

Udupa,

Sen

2021

Preprint

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We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction U is much larger than the hopping, the effective Hamiltonian H ef f describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, H ef f is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings (Jα, J β , Jγ) on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry (TRS), H ef f is also found to have a chiral three-spin interaction in each triangle, with the coefficient C of the interaction having opposite signs on up-and down-pointing triangles. Thus periodic driving which breaks TRS can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters (Jα, J β , Jγ, C) depend on the amplitude, frequency and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (colinear and coplanar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.

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“…This has led to development of several perturbative schemes for computation of H F ; some of these include Magnus expansion [5], adiabatic-impulse JHEP05(2021)172 approximation [27], the Hamilton flow method [28], and the Floquet perturbation theory (FPT) [29,30]. Out of these methods, the Floquet perturbation theory has the advantage of being easily applicable to a wide class of systems as well as being accurate over a large range of drive frequencies [31].…”

Section: Introductionmentioning

confidence: 99%

Conformal Floquet dynamics with a continuous drive protocol

Das

Ghosh

Sengupta

2021

J. High Energ. Phys.

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We study the properties of a conformal field theory (CFT) driven periodically with a continuous protocol characterized by a frequency ωD. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator U. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for U that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability (Pn), equal (Cn) and unequal (Gn) time two-point primary correlators, energy density(En), and the mth Renyi entropy ($$ {S}_n^m $$ S n m ) after n drive cycles. Our results show that below a crossover stroboscopic time scale nc, Pn, En and Gn exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of Cn, Gn and En for the continuous protocol and find emergence of spatial divergences of Cn and Gn in both the heating and non-heating phases. We express our results for $$ {S}_n^m $$ S n m and Cn in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

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Floquet perturbation theory for periodically driven weakly interacting fermions

Cited by 26 publications

References 69 publications

Analytic approaches to periodically driven closed quantum systems: methods and applications

Analytic approaches to periodically driven closed quantum systems: methods and applications

Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term

Conformal Floquet dynamics with a continuous drive protocol

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