Super Efimov effect of resonantly interacting fermions in two dimensions

Abstract

We study a system of spinless fermions in two dimensions with a short-range interaction fine-tuned to a p-wave resonance. We show that three such fermions form an infinite tower of bound states of orbital angular momentum l=\pm1 and their binding energies obey a universal doubly exponential scaling E_3^{(n)}\propto\exp(-2e^{3\pi n/4+\theta}) at large n. This "super Efimov effect" is found by a renormalization group analysis and confirmed by solving the bound state problem. We also provide an indication that there are l=\pm2 four-body resonances associated with every three-body bound state at E_4^{(n)}\propto\exp(-2e^{3\pi n/4+\theta-0.188}). These universal few-body states may be observed in ultracold atom experiments and should be taken into account in future many-body studies of the system.