Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions

Pierre Le Doussal, Naftali R. Smith, Nathan Argaman

We consider a system of $N$ spinless fermions, interacting with each other via a power-law interaction $\epsilon /r^n$, and trapped in an external harmonic potential $V(r)=r^2/2$, in $d=…