Interaction-Driven Shift and Distortion of a Flat Band in an Optical Lieb Lattice

Ozawa, Hideki; Taie, Shintaro; Ichinose, Takashi; Takahashi, Yoshiro

doi:10.1103/physrevlett.118.175301

Cited by 83 publications

(68 citation statements)

References 28 publications

(31 reference statements)

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“…Typically, the systems are engineered to faithfully realize exotic tight-binding models with multiple orbitals or atoms per unit cell, as well as complex lattice geometries. In these artificial systems, direct imaging of localized states [4,7,8] or the study of tunable interaction-induced effects [9] are few examples which show approaches hitherto not easily realizable in conventional condensed matter systems.…”

Section: Introductionmentioning

confidence: 99%

Dirac points emerging from flat bands in Lieb-kagome lattices

et al. 2020

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The energy spectra for the tight-binding models on the Lieb and kagomé lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for the Lieb lattice is distorted, generating two pairs of Dirac points. While the upper pair evolves into graphene-like Dirac cones in the kagomé limit, the low energy pair evolves until it merges producing the band-bottom flat band. The topological characterization of the Dirac points is achieved by projecting the Hamiltonian on the two relevant bands in order to obtain an effective Dirac Hamiltonian. The low energy pair of Dirac points is particularly interesting in this respect: when they emerge, they have opposite winding numbers, but as they merge, they have the same winding number. This apparent paradox is due to a continuous rotation of their states in pseudo-spin space, characterized by a winding vector. This simple, but quite rich model, suggests a way to a systematic characterization of two-band contact points in multiband systems.

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Section: Introductionmentioning

confidence: 99%

Dirac points emerging from flat bands in Lieb-kagome lattices

et al. 2020

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“…1. The noninteracting 2D Lieb lattice has been realized using ultracold atoms [17,26], photonic lattices [27,28], and also electronically [29,30]. To explore flat-band ferromagnetism, the repulsive Hubbard model on the 2D Lieb lattice has previously been studied using real-space dynamical mean theory (R-DMFT) combined with a numerical renormalization group (NRG) impurity solver at half-filling and zero temperature [6].…”

Section: Introductionmentioning

confidence: 99%

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

2017

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The properties of a phase at finite interactions can be significantly influenced by the underlying dispersion of the noninteracting Hamiltonian. We demonstrate this by studying the repulsive Hubbard model on the twodimensional Lieb lattice, which has a flat band for vanishing interaction U . We perform real-space dynamical mean-field theory calculations at different temperatures and dopings using a continuous-time quantum Monte Carlo impurity solver. Studying the frequency dependence of the self-energy, we find that a nonmagnetic metallic region at finite temperature displays non-Fermi-liquid behavior, which is a concomitant of the flat-band singularity. At half-filling, we also find a magnetically ordered region, where the order parameter varies linearly with the interaction strength, and a strongly correlated Mott insulating phase. The double occupancy decreases sharply for small U , highlighting the flat-band contribution. Away from half-filling, we observe the stripe order, i.e., an inhomogeneous spin and charge density wave of finite wavelength, which turns into a sublattice ordering at higher temperatures.

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“…Due to the high degeneracy and complete localization, FBs have relevance in many technolog-ical applications, such as diffraction-free propagation of light [47,48], enhanced light-matter interaction, generating slow light [49], etc. Although the theoretical proposal on the existence of FBs in certain periodic lattice geometries has been known for a long time, interest has been renewed in recent times with the experimental realization of FBs in a variety of photonic lattices [47,48,[50][51][52][53][54][55], ultracold atoms in optical lattices [56][57][58], and excitonpolariton condensates [59,60]. Also, from the experimental point of view, in particular, for optics experiments, nonlinear effects are relatively easy to probe in a system with nondispersive bands.…”

Section: Introductionmentioning

confidence: 99%

“…Apart from these, recently people have come up with new flat-band models based on a real organic material platform [61][62][63][64][65][66], for which they have discussed the appearance of intriguing flat-band states adopting density functional theory based calculations as well as tight-binding analysis. Over the course of time, a wide variety of lattice models have been reported to exhibit FBs in their band structure, among which the Lieb lattice has been one of the most popular, and it has been explored with vigor to accomplish various interesting physical properties of this lattice model [41,45,47,48,52,55,57,58]. A conventional Lieb lattice has three atomic sites per unit cell and can be thought to originate out of a square lattice.…”

Section: Introductionmentioning

confidence: 99%

Flat bands and nontrivial topological properties in an extended Lieb lattice

Bhattacharya

Pal

2019

Phys. Rev. B

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We report the appearance of multiple numbers of completely flat band states in an extended Lieb lattice model in two dimensions with five atomic sites per unit cell. We also show that this edge-centered square lattice can host intriguing topologically nontrivial phases when intrinsic spinorbit (ISO) coupling is introduced in the microscopic description of the corresponding tight-binding Hamiltonian of the system. This ISO coupling strength acts like a complex next-nearest-neighbor hopping term for this model and can be, in principle, tuned in a real-life experimental setup. In the presence of this ISO coupling, the band spectrum of the system gets gapped out, leading to nonzero integer values of the spin Chern number for different bands, indicating the nontrivial topological properties of the system. Furthermore, we show that for certain values of the ISO coupling, nearly flat bands with nonzero Chern numbers emerge in this lattice model. This opens up the possibility of realizing interesting fractional quantum spin Hall physics in this model when interaction is taken into account. This study might be very useful in an analogous optical lattice experimental setup. A possible application of our results can also be anticipated in the field of photonics using single-mode photonic waveguide networks. * ; Present address: Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.

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Interaction-Driven Shift and Distortion of a Flat Band in an Optical Lieb Lattice

Cited by 83 publications

References 28 publications

Dirac points emerging from flat bands in Lieb-kagome lattices

Dirac points emerging from flat bands in Lieb-kagome lattices

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

Flat bands and nontrivial topological properties in an extended Lieb lattice

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