2025/01/24 by Dupuis, Nicolas, Bhateja, Moksh, Rançon, Adam
#FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas)
paper · doi:10.48550/arxiv.2501.14887
We present a strong-coupling expansion of the Bose-Hubbard model based on a mean-field treatment of the hopping term, while onsite fluctuations are taken into account exactly. This random phase approximation (RPA) describes the universal features of the generic Mott-insulator--superfluid transition (induced by a density change) and the superfluid state near the phase transition. The critical quasi-particles at the quantum critical point have a quadratic dispersion with an effective mass m^* and their mutual interaction is described by an effective s-wave scattering length a^*. The singular part of the pressure takes the same form as in a dilute Bose gas, provided we replace the boson mass m and the scattering length in vacuum a by m^* and a^*, and the density n by the excess density |n-n\rm MI| of particles (or holes) with respect to the Mott insulator. We define a ``universal'' two-body contact C\rm univ that controls the high-momentum tail ∼ 1/|\bf k|4 of the singular part n\rm sing\bf k of the momentum distribution. We also apply the strong-coupling RPA to a lattice model of hard-core bosons and find that the high-momentum distribution is controlled by a universal contact, in complete agreement with the Bose-Hubbard model. Finally, we discuss a continuum model of bosons in an optical lattice and define two additional two-body contacts: a short-distance ``universal'' contact C\rm univ\rm sd which controls the high-momentum tail of n\rm sing\bf k at scales larger than the inverse lattice spacing, and a ``full'' contact C which controls the high-momentum tail of the full momentum distribution n\bf k.