  We show that rotating two-dimensional Fermi gases possess a nonrelativistic
scale and conformal invariance at weak but nonzero interactions, where the
scale invariance of universal short-range interactions is not yet broken by
quantum effects. We demonstrate the symmetry in the excitation spectrum of
few-fermion ensembles in a harmonic trap obtained by exact diagonalization. The
excitation spectrum is shown to split in a set of primary states and derived
excited states that consist of breathing modes as well as two different
center-of-mass excitations, which describe cyclotron and guiding-center
excitations of the total particle cloud. Furthermore, the conformal symmetry is
manifest in the many-body wave function, where it dictates the form of the
hyperradial component, which we demonstrate using Monte Carlo sampling of
few-body wave functions.
