Universality and scaling in the $N$-body sector of Efimov physics

Abstract

Universal behaviour has been found inside the window of Efimov physics for systems with $N=4,5,6$ particles. Efimov physics refers to the emergence of a number of three-body states in systems of identical bosons interacting {\it via} a short-range interaction becoming infinite at the verge of binding two particles. These Efimov states display a discrete scale invariance symmetry, with the scaling factor independent of the microscopic interaction. Their energies in the limit of zero-range interaction can be parametrized, as a function of the scattering length, by a universal function. We have found, using a particular form of finite-range scaling, that the same universal function can be used to parametrize the energies of $N\le 6$ systems inside the Efimov-physics window. Moreover, we show that the same finite-scale analysis reconciles experimental measurements of three-body binding energies with the universal theory.

Comments: Added the derivation of the three-body shift Added calculations with Poschl-Teller potential Added the analysis of Li7 trimer-binding energy experimental data [PRL 108, 210406 (2012)]