ONE-LOOP RENORMALIZATION GROUP ANALYSIS OF BOSE-FERMI MIXTURES

A weakly interacting Bose-Fermi mixture model was investigated using Wisonian renormalization group (RG). This model includes one boson-boson interaction term and one boson-fermion interaction term. The scaling dimensions of the two interaction coupling constants were calculated as 2-D at tree level and the flow equations were derived at one-loop level. We find that in the flow equations the contributions from the fermion loops go to zero as the length scale approaches infinity. In three-dimensional case two fixed points are calculated. One is the Gaussian fixed point and the other one is Wilson-Fisher fixed point. We observe that the boson-fermion interaction decouples at the Wilson-Fisher fixed point. We also find that under RG transformation the boson-fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson-fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.