Renormalization group study of the four-body problem

TL;DR

This paper uses renormalization group analysis to demonstrate that the four-boson problem at unitarity exhibits universal behavior, independent of four-body parameters, confirming recent conjectures from a theoretical perspective.

Contribution

It provides a renormalization group perspective confirming the universality of the four-boson problem at unitarity, including relations between bound states.

Findings

Four-body problem is universal at unitarity.

Derived relations between four- and three-body bound states.

Calculated the full bound state spectrum.

Abstract

We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length is infinite and all energies are at the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of Platter et al. and von Stecher et al. that the four-body problem is universal, now also from a renormalization group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound state spectrum and comment on the influence of effective range corrections.