Helium Atoms in Zeolite Cages: Novel Mott-Hubbard and Bose-Hubbard Systems

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 $T$.