Interacting Bose Gases Near Four Spatial Dimensions

Recently, interacting Bose gases at large positive scattering lengths can be experimentally investigated on the upper branch of a Feshbach resonance, which motivated more theoretical work. We proposed a new perspective to this problem by turning to $4$ spatial dimensions, and established a controllable expansion near $4$ spatial dimensions based on a $4-\epsilon$ analysis. Solving for the chemical potential shows the existence of a critical scattering length, at which the chemical potential reaches a maximum value and the many-body instability sets in. This is consistent with the result obtained by one of the authors (F.Z.) and his collaborators in $3$ dimensions.