The Fibonacci quasicrystal: case study of hidden dimensions and multifractality

Jagannathan, Anuradha

doi:10.48550/arxiv.2012.14744

Cited by 7 publications

(8 citation statements)

References 88 publications

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“…While for the quasiperiodic structures with 7-, 9-, 18-fold symmetry, the dimension of the embedding spaces increases [4][5][6] to six, n = 6. The Fibonacci tiling [7,8] does not fall in the above class of lattice potentials given by (10). However, the Fourier transform of the Fibonacci sequence has δ-function peaks at k = 2π (m + m'τ)/ , where τ = (1 + )/2 is the golden mean and m and m' are integers [9].…”

Section: Quasicrystalsmentioning

confidence: 99%

Bose-Einstein Condensation and Quasicrystals

Alexanian

Mkrtchian

2021

Armenian Journal of Physics

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We consider interacting Bose particles in an external local potential. It is shown that large class of external quasicrystal potentials cannot sustain any type of Bose-Einstein condensates. Accordingly, at spatial dimensions D ≤ 2 in such quasicrystal potentials a supersolid is not possible via Bose-Einstein condensates at finite temperatures. The latter also hold true for the two-dimensional Fibonacci tiling. However, supersolids do arise at D ≤ 2 via Bose-Einstein condensates from infinitely long-range, nonlocal interparticle potentials.

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Section: Quasicrystalsmentioning

confidence: 99%

Bose-Einstein Condensation and Quasicrystals

Alexanian

Mkrtchian

2021

Armenian Journal of Physics

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“…For example there is no delocalization-localization transition in the Fibonacci model. Instead, the Fibonacci potential induces critical behavior of all eigenstates at every potential strength [6,18,[26][27][28][29]. The transport exponents show a smooth crossover from ballistic to sub-diffusive with increase in the potential strength [27,30,31].…”

Section: Introductionmentioning

confidence: 96%

Quantum dynamics in the interacting Fibonacci chain

Chiaracane,

Pietracaprina,

Purkayastha

et al. 2021

Preprint

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Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultra-cold atom experiments where non trivial localised phases have been observed. One such quasiperiodic model is the so called Fibonacci model. In this tight-binding model, non-interacting particles are subject to on-site energies generated by a Fibonacci sequence. This is known to induce critical states, with a continuously varying dynamical exponent, leading to anomalous transport. In this work, we investigate whether anomalous diffusion present in the non-interacting system survives in the presence of interactions and establish connections to a possible transition towards a localized phase. We investigate the dynamics of the interacting Fibonacci model by studying real-time spread of density-density correlations at infinite temperature using the dynamical typicality approach. We also corroborate our findings by calculating the participation entropy in configuration space and investigating the expectation value of local observables in the diagonal ensemble.

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“…In contrast, fermion chains subjected to quasiperiodic potential exhibit a localization-delocalization transition at a finite potential strength [3][4][5][6][7][8][9][10][11][12][13][14][15] . Localization in such 1D fermion chains with quasiperiodic potentials has been studied extensively in the past [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . In recent times, such systems have also been experimentally realized using ultracold atom chains [20][21][22][23] .…”

Section: Introductionmentioning

confidence: 99%

Signatures of multifractality in a periodically driven interacting Aubry-André model

et al. 2022

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We study the many-body localization (MBL) transition of Floquet eigenstates in a driven, interacting fermionic chain with an incommensurate Aubry-André potential and a time-periodic hopping amplitude as a function of the drive frequency ωD using exact diagonalization (ED). We find that the nature of the Floquet eigenstates change from ergodic to Floquet-MBL with increasing frequency; moreover, for a significant range of intermediate ωD, the Floquet eigenstates exhibit non-trivial fractal dimensions. We find a possible transition from the ergodic to this multifractal phase followed by a gradual crossover to the MBL phase as the drive frequency is increased. We also study the fermion auto-correlation function, entanglement entropy, normalized participation ratio (NPR), fermion transport and the inverse participation ratio (IPR) as a function of ωD. We show that the auto-correlation, fermion transport and NPR displays qualitatively different characteristics (compared to their behavior in the ergodic and MBL regions) for the range of ωD which supports multifractal eigenstates. In contrast, the entanglement growth in this frequency range tend to have similar features as in the MBL regime; its rate of growth is controlled by ωD. Our analysis thus indicates that the multifractal nature of Floquet-MBL eigenstates can be detected by studying auto-correlation function and fermionic transport of these driven chains. We support our numerical results with a semi-analytic expression of the Floquet Hamiltonian obtained using Floquet perturbation theory (FPT) and discuss possible experiments which can test our predictions.

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The Fibonacci quasicrystal: case study of hidden dimensions and multifractality

Cited by 7 publications

References 88 publications

Bose-Einstein Condensation and Quasicrystals

Bose-Einstein Condensation and Quasicrystals

Quantum dynamics in the interacting Fibonacci chain

Signatures of multifractality in a periodically driven interacting Aubry-André model

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