Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

Bukov, Marin; Kolodrubetz, Michael; Polkovnikov, Anatoli

doi:10.1103/physrevlett.116.125301

Cited by 198 publications

(220 citation statements)

References 89 publications

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“…In the strongly interacting regime, the driving can induce the formation and dissociation of doublons. These processes involve the absorption and emission of photons with a probability amplitude proportional to J l (2Eδ/ω) [33]. Thus, for small driving amplitudes, 2Eδ < ωl = U (where δ is the distance between neighboring sites and l is the order of resonance), the probability is very small, and doublons persist in time.…”

Section: Modelmentioning

confidence: 99%

“…A different effective Hamiltonian is obtained depending on whether the system is in the strongly interacting regime (U ω > J ) or the high-frequency regime (ω U > J ). In the first case it corresponds to first performing the SWT and then a hopping renormalization, whereas in the second it is the other way around [32,33]. In the strongly interacting regime, the driving can induce the formation and dissociation of doublons.…”

Section: Modelmentioning

confidence: 99%

“…It is worth mentioning that these results could also be obtained by applying the HFE sequentially, integrating first the fast varying terms corresponding to the leading energy scale in the system [33]. We also note that higher-order corrections will include complex next-nearest-neighbor hoppings that break the time-reversal symmetry in systems without the presence of a magnetic flux.…”

mentioning

confidence: 99%

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Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

2017

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We analyze the dynamics of two strongly interacting fermions moving in two-dimensional lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon. We derive an effective Hamiltonian that allows us to understand the interplay between the interaction and the driving, revealing surprising effects that constrain the movement of the doublons. We show that it is possible to confine doublons to just the edges of the lattice and to a particular sublattice if different sites in the unit cell have different coordination numbers. Contrary to what happens in one-dimensional systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a nontrivial phase.

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Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

mentioning

confidence: 99%

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Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

2017

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“…The results obtained can be interpreted as in Ref. [42]. In fact, in the regime U, ω J, one can see that in a rotating frame defined by the canonical transformation V (t) = e −i(f (t) j jnj +U t j n ↑,j n ↓,j ) , the electron-electron interation U induces non-trivial phase shifts in the hopping amplitude.…”

Section: Numerical Resultsmentioning

confidence: 81%

Unconventional fermionic pairing states in a monochromatically tilted optical lattice

2017

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We study the one-dimensional attractive Fermionic Hubbard model under the influence of periodic driving with the time-dependent density matrix renormalization group method. We show that the system can be driven into an unconventional pairing state characterized by a condensate made of Cooper-pairs with a finite center-of-mass momentum similar to a Fulde-Ferrell state. We obtain results both in the laboratory and the rotating reference frames demonstrating that the momentum of the condensate can be finely tuned by changing the ratio between the amplitude and the frequency of the driving. In particular, by quenching this ratio to the value corresponding to suppression of the tunnelling and the Coulomb interaction strength to zero, we are able to "freeze" the condensate. We finally study the effects of different initial conditions, and compare our numerical results to those obtained from a time-independent Floquet theory in the large frequency regime. Our work offers the possibility of engineering and controlling unconventional pairing states in fermionic condensates.

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“…The effects of interactions between electrons in periodically driven systems have received much attention in recent times [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63] . It has been shown that a sinusoidal perturbation of the Hubbard model can lead to coherent destruction of tunneling, creation of gauge fields, and density-dependent tunneling 64 .…”

Section: Introductionmentioning

confidence: 99%

Effects of interactions on periodically driven dynamically localized systems

Agarwala

Sen

2017

Phys. Rev. B

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It is known that there are lattice models in which non-interacting particles get dynamically localized when periodic δ-function kicks are applied with a particular strength. We use both numerical and analytical methods to study the effects of interactions in three different models in one dimension. The systems we have considered include spinless fermions with interactions between nearest-neighbor sites, the Hubbard model of spin-1/2 fermions, and the Bose Hubbard model with on-site interactions. We derive effective Floquet Hamiltonians up to second order in the time period of kicking. Using these we show that interactions can give rise to a variety of interesting results such as two-body bound states in all three models and dispersionless few-particle bound states with more than two particles for spinless fermions and bosons. We substantiate these results by exact diagonalization and stroboscopic time evolution of systems with a few particles.We derive a pseudo-spin-1/2 limit of the Bose Hubbard system in the thermodynamic limit and show that a special case of this has an exponentially large number of degenerate eigenstates of the effective Hamiltonian. Finally we study the effect of changing the strength of the δ-function kicks slightly away from perfect dynamical localization; we find that a single particle remains dynamically localized for a long time after which it moves ballistically.

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Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

Cited by 198 publications

References 89 publications

Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

Unconventional fermionic pairing states in a monochromatically tilted optical lattice

Effects of interactions on periodically driven dynamically localized systems

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