Scale and conformal invariance in rotating few-fermion systems

We show that rotating two-dimensional Fermi gases possess a nonrelativistic scale and conformal invariance at weak interactions, where the scale invariance of universal short-range interactions is not broken by quantum effects. We demonstrate the symmetry in the excitation spectrum of few-fermion ensembles in a harmonic trap obtained by exact diagonalization, which are constrained by the operator-state correspondence. The excitation spectrum is shown to split in a set of primary states, the energies of which correspond to scaling dimensions of conformal operators, 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.Comment: 16 pages, 10 figure