Three Identical Fermions with Resonant p-wave Interactions in Two Dimensions

TL;DR

This paper investigates the existence of super-Efimov states in a three-fermion system with resonant p-wave interactions in two dimensions, revealing their dependence on a specific potential parameter and challenging previous universality claims.

Contribution

The study provides an independent analysis using hyperspherical formalism, showing super-Efimov states only occur under a precise condition and clarifies the role of an emergent parameter.

Findings

Super-Efimov states exist only when the parameter Y equals zero.

For Y>0, bound state energies scale differently, as -(nπ)^2/2Y.

No shallow bound states are found when Y<0.

Abstract

A new kind of "super-Efimov" states of binding energies scaling as $\ln|E_n|\sim-e^{3n\pi/4}$ were predicted by a field theory calculation for three fermions with resonant $p$-wave interactions in two dimensions [Phys. Rev. Lett. \textbf{110}, 235301 (2013)]. However, the universality of these "super-Efimov" states has not been proved independently. In this Letter, we study the three fermion system through the hyperspherical formalism. Within the adiabatic approximation, we find that at $p$-wave resonances, the low energy physics of states of angular momentum $\ell=\pm1$ crucially depends on the value of an emergent dimensionless parameter $Y$ determined by the detail of the inter-particle potential. Only if $Y$ is exactly zero, the predicted "super-Efimov" states exist. If $Y>0$, the scaling of the bound states changes to $\ln|E_n|\sim-(n\pi)^2/2Y$, while there are no shallow bound states if $Y<0$.