Universal behaviour of four-boson systems from a functional renormalisation group

TL;DR

This paper uses a functional renormalisation group approach to study four-boson systems near the unitary limit, revealing multiple bound states and their scaling properties without dependence on a four-body parameter.

Contribution

It introduces a local effective action with a dynamical trimer field to analyze four-boson systems, aligning results with exact solutions and experiments, and uncovers an infinite hierarchy of four-body states.

Findings

Three four-body bound states found below the shallowest three-body state.

Two of the four-body states match exact solutions and experimental data.

An infinite number of four-body states follow a double-exponential scaling pattern.

Abstract

We apply a functional renormalisation group to systems of four bosonic atoms close to the unitary limit. We work with a local effective action that includes a dynamical trimer field and we use this field to eliminate structures that do not correspond to the Faddeev-Yakubovsky equations. In the physical limit, we find three four-body bound states below the shallowest three-body state. The values of the scattering lengths at which two of these states become bound are in good agreement with exact solutions of the four-body equations and experimental observations. The third state is extremely shallow. During the evolution we find an infinite number of four-body states based on each three-body state which follow a double-exponential pattern in the running scale. None of the four-body states shows any evidence of dependence on a four-body parameter.