Compact localized states and localization dynamics in the dice lattice

Zhang, S. M.; Jin, Lin

doi:10.1103/physrevb.102.054301

Cited by 21 publications

(7 citation statements)

References 74 publications

(101 reference statements)

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“…In particular, a dice lattice with lattice constant a 0 can be constructed by using six linearly polarized laser beams of wavelength λ = 3a 0 /2. Another plausible pathway for fabricating these lattices is the use of coupled resonators [17]. The prescription is the incorporation of additional resonators at the center of hexagonal rings of the honeycomb lattice.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The underlying mechanism behind such flat bands can be well explained in terms of destructive interference through various network paths. For example, the bipartite dice lattice [11][12][13][14][15][16][17][18][19][20] is one of the first and most prominent examples where such flat-band physics was introduced. In a dice lattice, atoms are not only placed at the vertices of hexagons but also at the centers.…”

Section: Introductionmentioning

confidence: 99%

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Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

2023

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The interplay of topology and non-Hermiticity has led to diverse, exciting manifestations in a plethora of systems. In this work, we systematically investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice. Due to the presence of a nondispersive flat band, the dice-Haldane model hosts a topologically rich phase diagram with the nontrivial phases accommodating Chern numbers ±2. We introduce non-Hermiticity into this model in two ways-through balanced non-Hermitian gain and loss, and by nonreciprocal hopping in one direction. Both these types of non-Hermiticity induce higher-order exceptional points of order three. Remarkably, the exceptional points at high-symmetry points occur at odd integer values of the non-Hermiticity strength in the case of balanced gain and loss, and at odd integer multiples of 1/ √ 2 for nonreciprocal hopping. We substantiate the presence and the order of these higher-order exceptional points using the phase rigidity and its scaling. Furthermore, we construct a phase diagram to identify and locate the occurrence of these exceptional points in the parameter space. Non-Hermiticity has yet more interesting consequences on a finite-sized lattice. Unlike for balanced gain and loss, in the case of nonreciprocal hopping, the nearest-neighbor lattice system under periodic boundary conditions accommodates a finite, nonzero spectral area in the complex plane. This manifests as the non-Hermitian skin effect when open boundary conditions are invoked. In the more general case of the dice-Haldane lattice model, the non-Hermitian skin effect can be caused by both gain and loss or nonreciprocity. Fascinatingly, the direction of localization of the eigenstates depends on the nature and strength of the non-Hermiticity. We establish the occurrence of the skin effect using the local density of states, inverse participation ratio, and the edge probability and demonstrate its robustness to disorder. Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

2023

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“…1 (f). These states are typical in tight-binding models with geometrical/configurational disorder and they have been found in several models [99], e.g., in random combs, random graphs, quantum spin-ice, and electronic models that host flat bands [25,26,70,[100][101][102][103][104][105][106][107][108][109][110]. In the present case, these states are generated by special local configurations of disorder (spins) [70].…”

Section: E ≈mentioning

confidence: 61%

Effects of critical correlations on quantum percolation in two dimensions

De Tomasi,

Hart,

Glittum

et al. 2022

Preprint

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We analyze the out-of-equilibrium dynamics of a quantum particle coupled to local magnetic degrees of freedom that undergo a classical phase transition. Specifically, we consider a two-dimensional tight-binding model that interacts with a background of classical spins in thermal equilibrium, which are subject to Ising interactions and act as emergent, correlated disorder for the quantum particle. Particular attention is devoted to temperatures close to the ferromagnet-to-paramagnet transition.To capture the salient features of the classical transition, namely the effects of long-range correlations, we focus on the strong coupling limit, in which the model can be mapped onto a quantum percolation problem on spin clusters generated by the Ising model. By inspecting several dynamical probes such as energy level statistics, inverse participation ratios, and wave-packet dynamics, we provide evidence that the classical phase transition might induce a delocalization-localization transition in the quantum system at certain energies. We also identify further important features due to the presence of Ising correlations, such as the suppression of compact localized eigenstates.

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“…In the noninteracting case, a purely flat band has constant energy as a function of quasimomentum. For a particle loaded in a flat band, the high degeneracy causes it to localize in a compact form within a few sites whose geometry depends on the details of the Hamiltonian [1][2][3][4]. Any finite interaction will be much larger than the bandwidth, leading to rich strongly-correlated physics at any value of the interaction strength.…”

Section: Introductionmentioning

confidence: 99%

Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands

Liang¹,

Yang²,

Chen³

et al. 2023

Preprint

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We investigate the superconductor-insulator transition (SIT) in disordered quasi-one dimensional systems using the density-matrix renormalization group method. Focusing on the case of an interacting spinful Hamiltonian at quarter-filling, we contrast the differences arising in the SIT when the parent non-interacting model features either flat or dispersive bands. Furthermore, by comparing disorder distributions that preserve or not SU(2)-symmetry, we unveil the critical disorder amplitude that triggers insulating behavior. While scaling analysis suggests the transition to be of a Berezinskii-Kosterlitz-Thouless type for all models (two lattices and two disorder types), only in the flat-band model with Zeeman-like disorder the critical disorder is nonvanishing. In this sense, the flat-band structure does strengthen superconductivity. For both flat and dispersive band models, i) in the presence of SU(2)-symmetric random chemical potentials, the disorder-induced transition is from superconductor to insulator of singlet pairs; ii) for the Zeeman-type disorder, the transition is from superconductor to insulator of unpaired fermions. In all cases, our numerical results suggest no intermediate disorder-driven metallic phase.

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Compact localized states and localization dynamics in the dice lattice

Cited by 21 publications

References 74 publications

Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

Effects of critical correlations on quantum percolation in two dimensions

Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands

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