T. Haugset et F. Ravndal, SCALE ANOMALIES IN NONRELATIVISTIC FIELD-THEORIES IN 2+1 DIMENSIONS, Physical review. D. Particles and fields, 49(8), 1994, pp. 4299-4301
From the one-loop effective potential for a gas of nonrelativistic bos
ons in two spatial dimensions interacting via a delta-function potenti
al at zero temperature and finite chemical potential, the anomaly of t
he energy-momentum tensor follows directly. It is also similarly deriv
ed when the bosons have an additional Chem-Simons interaction. In the
special case of anyons, the scale anomaly vanishes to one-loop order i
n the effective potential and also to second order in the statistical
angle.