Super Efimov effect of resonantly interacting fermions in two dimensions

TL;DR

This paper predicts a novel super Efimov effect in two-dimensional resonant fermionic systems, revealing an infinite series of universal bound states with doubly exponential energy scaling, confirmed through renormalization group analysis and bound state calculations.

Contribution

It introduces the super Efimov effect for 2D fermions at p-wave resonance, a new universal phenomenon with an infinite tower of bound states and associated four-body resonances.

Findings

Infinite tower of three-body bound states with doubly exponential energy scaling.

Presence of four-body resonances linked to three-body states.

Potential observability in ultracold atom experiments.

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.