Mobility edge of the two-dimensional Bose-Hubbard model

Geißler, Andreas; Pupillo, Guido

doi:10.1103/physrevresearch.2.042037

Cited by 14 publications

(6 citation statements)

References 55 publications

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“…6 demonstrates that the excited states exhibit a mobility edge separating localised and delocalised states. This is consistent with what is seen in generalised Aubre-Andry Models [13,14,27]. b. Hubbard parameters While numerical simulations based on the interacting BH Hamiltonian will be left to future work, we can already gain physical insight by inspecting the distributions of on-site energies p( ), interactions p(U ) and tunneling amplitudes p(J ij ), see Fig.…”

Section: B Bose-hubbard Modelsupporting

confidence: 81%

“…Constructing exact tight-binding models for general quasicrystals is difficult because (a) one cannot use Bloch's theorem to construct appropriate Wannier functions and (b) the lack of periodicity typically prevents one from efficiently describing their thermodynamic limit. Several quasiperiodic models, such as Aubry-André models [10,13,14,[25][26][27], are explicitly constructed using quasiperiodic perturbations of an initially periodic lattice and thereby inherit the original Wannier functions. These models however represent only particular limits of general quasicrystalline potentials.…”

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confidence: 99%

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Hubbard Models for Quasicrystalline Potentials

Gottlob¹,

Schneider²

2022

Preprint

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Quasicrystals are long-range ordered, yet not periodic, and thereby present a fascinating challenge for condensed matter physics, as one cannot resort to the usual toolbox based on Bloch's theorem. Here, we present a numerical method for constructing the Hubbard Hamiltonian of non-periodic potentials without making use of Bloch's theorem and apply it to the case of an eightfold rotationally symmetric 2D optical quasicrystal that was recently realized using cold atoms. We construct maximally localised Wannier functions and use them to extract on-site energies, tunneling amplitudes, and interaction energies. In addition, we introduce a configuration-space representation, where sites are ordered in terms of shape and local environment, that leads to a compact description of the infinite-size quasicrystal in which all Hamiltonian parameters can be expressed as smooth functions. This configuration-space picture allows one to construct arbitrarily large tight-binding graphs for numerical many-body calculations and enables new analytic arguments on the topological structure and many-body physics of these models, for instance the conclusion that this quasicrystal will host unit-filling Mott insulators in the thermodynamic limit.

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Section: B Bose-hubbard Modelsupporting

confidence: 81%

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confidence: 99%

Hubbard Models for Quasicrystalline Potentials

Gottlob¹,

Schneider²

2022

Preprint

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“…The 2D MBL was suggested to be unstable towards a crossover to ergodicity on very long time scales 100 . Several numerical approaches were proposed to address the 2D problem 68,71,[101][102][103][104][105][106] . This paper follows the approach of simulating the time evolution of a 2D MBL system with the iPEPS tensor network 68,71,103,105,106 but it employs the NTU algorithm 73 .…”

Section: Many Body Localizationmentioning

confidence: 99%

Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update

Dziarmaga

2021

Preprint

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“…Most previous studies of MEs have been concerned with the 1D cases; however, little is known about that in the 2D QCs, though some numerical evidences show the existence of MEs in 2D systems [84][85][86][87]. The aim of this Letter is to disclose the exact MEs in 2D QCs, described by the 2D parity-time (PT ) symmetric QCs with two incommensurate modulation frequencies along the x-and y-directions.…”

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confidence: 97%

Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals

Xu,

Xia,

Chen

2021

Preprint

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The emergence of the mobility edge (ME) has been recognized as an important characteristic of Anderson localization. The difficulty in understanding the physics of the MEs in three-dimensional (3D) systems from a microscopic picture promotes discovering of models with the exact MEs in lowerdimensional systems. While most of previous studies concern on the one-dimensional (1D) quasiperiodic systems, the analytic results that allow for an accurate understanding of two-dimensional (2D) cases are rare. In this Letter, we disclose an exactly solvable 2D quasicrystal model with parity-time (PT ) symmetry displaying exact MEs. In the thermodynamic limit, we unveil that the extendedlocalized transition point, observed at the PT symmetry breaking point, is of topological nature characterized by a hidden winding number defined in the dual space. The 2D non-Hermitian quasicrystal model can be realized in the coupling waveguide platform, and the localization features can be detected by the excitation dynamics.

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Mobility edge of the two-dimensional Bose-Hubbard model

Cited by 14 publications

References 55 publications

Hubbard Models for Quasicrystalline Potentials

Hubbard Models for Quasicrystalline Potentials

Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update

Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals

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