Revealing the origin of super-Efimov states in the hyperspherical formalism

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Super-Efimov states are a new kind of universal three-body bound states predicted for three identical fermions with p-wave resonant interactions in two dimensions by a recent field-theoretic calculation [Phys. Rev. Lett. 110, 235301 (2013)]. The binding energies of these states obey a dramatic double exponential scaling Eₙ=E*(-2 eπⁿ/ˢ⁰⁺θ) with universal scaling s₀=4/3 and three-body parameters E* and θ. We use the hyperspherical formalism and show that the super-Efimov states originate from an emergent effective potential -1/4ρ²-(s₀²+1/4)/ρ²²(ρ) at large hyperradius ρ. Moreover, for pairwise interparticle potentials with van der Waals tails, our numerical calculation indicates that the three-body parameters E* and θ are also universal and the ground super-Efimov state shall cross the threshold when the 2D p-wave scattering area is about -42.0 lᵥdW² with lᵥdW the van der Waals length.