Revealing the origin of super Efimov states in the hyperspherical formalism

摘要

Super Efimov states are new kinds of universal three-body bound states predicted for three identical fermions with p-wave resonant interactions in two dimensions (2D) by a recent field-theoretic calculation [Phys. Rev. Lett. 110, 235301 (2013)]. The binding energies of these states obey a dramatic double exponential scaling E-n = E-* exp(-2e(pi n/s0+theta)) with universal scaling s(0) = 4/3 and three-body parameters E-* and theta. We use the hyperspherical formalism and show that the super Efimov states originate from an emergent effective potential -1/4 rho(2) - (s(0)(2) + 1/4)/rho(2) ln(2)(rho) at large hyperradius rho. Moreover, for pairwise interparticle potentials with van der Waals tails, our numerical calculation indicates that the three-body parameters E-* and theta are also universal and the ground super Efimov state shall cross the threshold when the 2D p-wave scattering area is about -42.0l(vdW)(2), with l(vdW) the van der Waals length.