Low-lying excitations of ${}^{4}$ He and ${}^{3}$ He atoms confined inside zeolite cages have been modeled by Bose-Hubbard and Mott-Hubbard rings with strong intrasite repulsion and finite intersite attraction. Differences between ${}^{4}$ He and ${}^{3}$ He arise due to mass and the statistics. Calculated temperature and concentration dependences of the heat capacity agree qualitatively with the experiment, but a quantitative comparison suggests that disorder may dominate at very low $T$ .Low-lying excitations of ${}^{4}$He and ${}^{3}$He atoms confined inside zeolite cages have been modeled by Bose-Hubbard and Mott-Hubbard rings with strong intrasite repulsion and finite intersite attraction. Differences between ${}^{4}$He and ${}^{3}$He arise due to mass and the statistics. Calculated temperature and concentration dependences of the heat capacity agree qualitatively with the experiment, but a quantitative comparison suggests that disorder may dominate at very low $T$.

Physical Review LettersJul 17, 199556 citations

Tunable Statistics-Induced Caging in the Anyon-Hubbard Model

Zenong Zhou, Chaorong Guo, Hongzheng Wu +2 more

We study the quantum dynamics of two interacting anyons in the Anyon-Hubbard model on a four-site plaquette, a system that is exactly mappable to a Bose-Hubbard model. We reveal that static Aharonov-Bohm (AB) caging, induced by only specific statistical phases, emerges in the strongly interacting limit but breaks down under weak interparticle interactions. To address this, we demonstrate that statistical-factor-induced AB caging can be dynamically restored via Floquet engineering. This dynamical mechanism, governed by the synthetic Floquet flux and the anyonic statistical phase, extends the caging effect into the weakly interacting regime across the full spectrum of statistical phases. Furthermore, we show that the external drive enables the selective caging of anyons, providing an efficient approach for manipulating anyons and identifying statistical phases.We study the quantum dynamics of two interacting anyons in the Anyon-Hubbard model on a four-site plaquette, a system that is exactly mappable to a Bose-Hubbard model. We reveal that static Aharonov-Bohm (AB) caging, induced by only specific statistical phases, emerges in the strongly interacting limit but breaks down under weak interparticle interactions. To address this, we demonstrate that statistical-factor-induced AB caging can be dynamically restored via Floquet engineering. This dynamical mechanism, governed by the synthetic Floquet flux and the anyonic statistical phase, extends the caging effect into the weakly interacting regime across the full spectrum of statistical phases. Furthermore, we show that the external drive enables the selective caging of anyons, providing an efficient approach for manipulating anyons and identifying statistical phases.

quant-pharXiv:2608.15739Aug 18, 20260 citations

Hubbard model for ultracold atoms

Anonymous

PhysicsMar 15, 20100 citations

Superexchange in Mott-Hubbard Insulators

Demetra Psiachos

arXiv:1407.3665Jul 14, 20140 citations

Disordered Hubbard Model with Ultracold Atoms

William McGehee, Stanimir Kondov, Brian DeMarco

Bulletin of the American Physical SocietyJun 6, 20130 citations

Two-dimensional Bose-Hubbard model for helium on graphene

Jiangyong Yu, Ethan Lauricella, Mohamed M. Elsayed +9 more

An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a system of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons $(U\ensuremath{\approx}\ensuremath{\infty})$, repulsive nearest-neighbor $(V>0)$ and small attractive $({V}^{\ensuremath{'}}<0)$ next-nearest-neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively pointlike, the detailed microscopic form of the short-range electrostatic and long-range dispersion interactions in the helium-graphene system is crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of $^{4}\mathrm{He}$ adsorbed on graphene deep in the commensurate solid phase with $1/3$ of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a system of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons $(U\ensuremath{\approx}\ensuremath{\infty})$, repulsive nearest-neighbor $(V>0)$ and small attractive $({V}^{\ensuremath{'}}<0)$ next-nearest-neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively pointlike, the detailed microscopic form of the short-range electrostatic and long-range dispersion interactions in the helium-graphene system is crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of $^{4}\mathrm{He}$ adsorbed on graphene deep in the commensurate solid phase with $1/3$ of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.

arXiv:2102.11288Physical review. B./Physical review. BJun 9, 202114 citations

Low-lying excitations of

{}^{4}

He and

{}^{3}

He atoms confined inside zeolite cages have been modeled by Bose-Hubbard and Mott-Hubbard rings with strong intrasite repulsion and finite intersite attraction. Differences between

{}^{4}

He and

{}^{3}

He arise due to mass and the statistics. Calculated temperature and concentration dependences of the heat capacity agree qualitatively with the experiment, but a quantitative comparison suggests that disorder may dominate at very low

T

(V>0)

and small attractive $({V}^{\ensuremath{'}}<0)$ next-nearest-neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively pointlike, the detailed microscopic form of the short-range electrostatic and long-range dispersion interactions in the helium-graphene system is crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of

^{4}\mathrm{He}

adsorbed on graphene deep in the commensurate solid phase with

1/3

of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.