Hubbard Models for Quasicrystalline Potentials

Abstract

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.

9 pages, 12 figures, plus appendix; minor changes

References in corpus (16)

• Many body localization and thermalization in quantum statistical mechanics
• Non-standard Hubbard models in optical lattices: a review
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Recent progress in many-body localization
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: from superfluidity to density waves
• Quantum glass phases in the disordered Bose-Hubbard model
• Spin waves and local magnetizations on the Penrose tiling
• Topological Properties of Ultracold Bosons in One-Dimensional Quasiperiodic Optical Lattice
• A note on the quasiperiodic many-body localization transition in dimension $d>1$
• Quantum simulation of a 2D quasicrystal with cold atoms
• Bosons in a two-dimensional bichromatic quasiperiodic potential: Analysis of the disorder in the Bose-Hubbard parameters and phase diagrams
• Construction of Maximally Localized Wannier Functions

Cited by in corpus (17)

• Observing the two-dimensional Bose glass in an optical quasicrystal
• Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential
• Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals
• Quasicrystalline Bose glass in the absence of disorder and quasidisorder
• Colloquium: Synthetic quantum matter in non-standard geometries
• Properties of the Ammann-Beenker tiling and its square approximants
• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Hubbard parameters for programmable tweezer arrays
• Multifractality and Hyperuniformity in Quasicrystalline Bose-Hubbard Models with and without Disorder
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Quasiperiodicity protects quantized transport in disordered systems without gaps
• Renormalization view on resonance proliferation between many-body localized phases
• Effective tight-binding models in optical moiré potentials
• On the origin of energy gaps in quasicrystalline potentials
• Site-selective correlations in interacting "flat-band" quasicrystals
• Localization and topological signatures under periodic twisting