Simple method to construct flat-band lattices

Morales‐Inostroza, Luis; Vicencio, Rodrigo A.

doi:10.1103/physreva.94.043831

Cited by 93 publications

(103 citation statements)

References 44 publications

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“…Such a localized particle can be regarded as a concrete example of a flat-band compactons. More general discussion and construction for the flat-band compactons have been given in [51,52];…”

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confidence: 99%

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

2020

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We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced manybody localizated phase. Physical picture of this crossover is investigated in detail. We also observe nonergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.

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confidence: 99%

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

2020

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“…The compact localized states occupy only four sites (B, C, E, and F) of a unit cell, with equal intensity and the following phase distributions: {+, +, −, −} for the upper and {+, −, +, −} lower FBs, respectively. We can easily identify the destructive interference at sites A n and D n , as expected considering the properties of mini-arrays [28]. When exciting these localized FB states, the transport is absolutely canceled across the lattice due to the perfectly zero amplitude at the connector sites.…”

Section: The Modelmentioning

confidence: 60%

“…(NN) interactions preserve the flatness of the band. This requires a high degree of symmetry in order to effectively cancel the transport at different connector sites [28].…”

Section: Introductionmentioning

confidence: 99%

Observation of localized ground and excited orbitals in graphene photonic ribbons

et al. 2018

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We report on the experimental realization of a quasi-one-dimensional photonic graphene ribbon supporting four flat-bands (FBs). We study the dynamics of fundamental and dipolar modes, which are analogous to the s and p orbitals, respectively. In the experiment, both modes (orbitals) are effectively decoupled from each other, implying two sets of six bands, where two of them are completely flat (dispersionless). Using an image generator setup, we excite the s and p FB modes and demonstrate their non-diffracting propagation for the first time. Our results open an exciting route towards photonic emulation of higher orbital dynamics.

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“…Again, the unit cell's CLSs lead to two tunable flat bands at energies given by the eigenvalues of Eq. (27), as shown in Fig.6 (b2).…”

Section: B Using Symmetries To Design Flat Bandsmentioning

confidence: 68%

Compact localized states and flat bands from local symmetry partitioning

2018

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Journal reference: Phys. Rev. B 97, 035161 (2018) We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states in an energy continuum and flat energy bands for periodically repeated local symmetries in one-and two-dimensional lattices. The framework is based on very recent theorems in graph theory which are here employed to obtain a block partitioning of the Hamiltonian induced by the symmetry of a given system under local site permutations. The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states. We distinguish between local symmetry operations which commute with the Hamiltonian, and those which do not commute due to an asymmetric coupling to the surrounding sites. While valuable as a computational tool for versatile discrete systems with locally symmetric structures, the approach provides in particular a unified, intuitive, and efficient route to the flexible design of compact localized states at desired energies.

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Simple method to construct flat-band lattices

Cited by 93 publications

References 44 publications

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

Observation of localized ground and excited orbitals in graphene photonic ribbons

Compact localized states and flat bands from local symmetry partitioning

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