Interaction-induced topological properties of two bosons in flat-band systems

Pelegrí, G.; Marques, A. M.; Ahufinger, V.; Mompart, J.; Dias, R. G.

doi:10.1103/physrevresearch.2.033267

Cited by 38 publications

(16 citation statements)

References 106 publications

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“…. Diagonalization of the Hamiltonian in ( 1) yields an all-bands flat energy spectrum 18 , shown in Fig. 1(c), as a consequence of an Aharonov-Bohm caging effect induced by the π-flux in each plaquette [19][20][21] .…”

Section: Diamond Chain With π-Flux Per Plaquettementioning

confidence: 99%

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One-dimensional $2^n$-root topological insulators and superconductors

Marques,

Madail,

Dias

2021

Preprint

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Square-root topology is a recently emerged sub-field describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite energy edge states of the starting square-root model inherit their topological features from the zero-energy edge states of a known topological insulator/superconductor present in the squared model. Focusing on one-dimensional models, we show how this concept can be generalized to 2 n -root topological insulators and superconductors, with n any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of 2 n -root topological insulators/superconductors which connects the Hamiltonian of the starting model for any n, through a series of squaring operations followed by constant energy shifts, to the Hamiltonian of the known topological insulator/superconductor, identified as the source of its topological features. Our work paves the way for an extension of 2 n -root topology to higher-dimensional systems.

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Section: Diamond Chain With π-Flux Per Plaquettementioning

confidence: 99%

“…The first term in ( 4) is quantized to either 0 or π such that, modulo 2π, one necessarily has γ ± = π 2 . The states of the zero-energy flat band n = 0, on the other hand, have no weight on the A sublattice 18 , so the usual π-quantization holds for γ 0 .…”

Section: Diamond Chain With π-Flux Per Plaquettementioning

confidence: 99%

One-dimensional $2^n$-root topological insulators and superconductors

Marques,

Madail,

Dias

2021

Preprint

Self Cite

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“…The physics of two-body bound states in the presence of a flat band has been recently explored theoretically in different contexts, including topological matter [17][18][19][20] and the link between the inverse effective mass of the bound state and the quantum metric of the singleparticle states [21][22][23]. This second direction is related to the more general question of understanding how transport and superconductivity can occur in system with quenched kinetic energy [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

Orso,

Singh

2021

Preprint

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We investigate pairing and superconductivity in the attractive Hubbard model on the onedimensional sawtooth lattice. This is a periodic lattice with two sites per unit cell, which exhibits a flat band (FB) by fine-tuning the hopping rates. We first discuss the formation of pairs in vacuum, showing that there is a broad region of hopping rates values around the FB point, for which both the binding energy and the effective mass of the bound state are strongly affected even by weak interactions. Based on the DMRG method, we then address the ground-state properties of a system with equal spin populations as a function of the interaction strength and the hopping rates. We compare our results with those available for a linear chain, where the model is integrable by Bethe ansatz, and show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. The chemical potential of a system near the FB point remains always close to its zero-density limit predicted by the two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the binding energy, it is no longer peaked at the FB point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. In particular, we find that three-body bound states (trimers) are allowed in the sawtooth lattice, in sharp contrast with the linear chain geometry.

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“…Furthermore, as the first step towards understanding topological many-body systems, one may judiciously focus on the simplest nontrivial subspace with interactions, that of only two excitations. Indeed, the two-excitation sector already provides some hallmarks of multi-excitation physics, such as bound two-particle states and novel bands in the quasiparticle bandstructure [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Doublons, topology and interactions in a one-dimensional lattice

Azcona,

Downing

2021

Preprint

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We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities and optical lattices, and provide perspectives for topological many-body physics.

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Interaction-induced topological properties of two bosons in flat-band systems

Cited by 38 publications

References 106 publications

One-dimensional $2^n$-root topological insulators and superconductors

One-dimensional $2^n$-root topological insulators and superconductors

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

Doublons, topology and interactions in a one-dimensional lattice

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