Bulk topological signatures of a quasicrystal

Rai, Gautam; Schlömer, Henning; Matsumura, Chris; Haas, Stephan; Jagannathan, Anuradha

doi:10.1103/physrevb.104.184202

Cited by 9 publications

(4 citation statements)

References 22 publications

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“…To overcome this limitation and arrive at a powerful, compact representation, we sort the lattices sites based on their shapes and local environments and arrive at a bounded configuration space that enables us to describe the infinite quasicrystal. This procedure is similar to configuration-space descriptions of stacked bilayer systems [30][31][32] and we demonstrate in Appendix H that it directly corresponds to the perpendicular space of discrete octagonal quasicrystals [33][34][35][36][37].…”

Section: Configuration Space: Describing the Quasicrystal In The Infi...mentioning

confidence: 78%

“…In addition we introduce a configurationspace description of this quasicrystal, where sites are ordered according to their shape and local environment, which allows to describe the infinite-size quasicrystal in terms of smooth functions in a compact parameter space. This method is similar to configuration-space descriptions employed for stacked bilayer systems [30][31][32] and the resulting description directly corresponds to perpendicular spaces widely used in the field of discrete quasicrystals [33][34][35][36][37].…”

mentioning

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: Configuration Space: Describing the Quasicrystal In The Infi...mentioning

confidence: 78%

mentioning

confidence: 99%

Hubbard Models for Quasicrystalline Potentials

Gottlob¹,

Schneider²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…To overcome this limitation and arrive at a powerful, compact representation, we sort the lattice sites based on their shapes and local environments and arrive at a bounded configuration space that enables us to describe the infinite quasicrystal. This procedure is similar to configurationspace descriptions of stacked bilayer systems [30][31][32] and we demonstrate in Appendix I that it directly corresponds to the perpendicular space of discrete octagonal quasicrystals [33][34][35][36][37].…”

Section: Configuration Space: Describing the Quasicrystal In The Infi...mentioning

confidence: 83%

“…In 70 addition, we introduce a configuration-space description of 71 this quasicrystal, where sites are ordered according to their 72 shape and local environment, which serves as an aperi-73 odic analog of the Brillouin zone, and allows to describe 74 the infinite-size quasicrystal in terms of smooth functions 75 in a compact parameter space. This method is similar to 76 configuration-space descriptions employed for stacked bilayer 77 systems [30][31][32] and the resulting description directly corre-78 sponds to perpendicular spaces widely used in the field of 79 discrete quasicrystals [33][34][35][36][37].…”

mentioning

confidence: 99%