Four-boson bound states from a functional renormalisation group

TL;DR

This paper employs the functional renormalisation group to analyze three- and four-boson bound states near the unitary limit, revealing qualitative similarities to exact methods but with some overbinding and a narrow third state.

Contribution

It introduces a novel approach using a running trimer field within the functional renormalisation group framework to study few-boson bound states.

Findings

Qualitative agreement with exact approaches

Overbinding of four-body states in the truncated model

Identification of a narrow third four-body state

Abstract

We use the functional renormalisation group to study the spectrum of three- and four-body states in bosonic systems around the unitary limit. Our effective action includes all energy-independent contact interactions in the four-atom sector and we introduce a running trimer field to eliminate couplings that involve the atom-atom-dimer channel. The results show qualitatively similar behaviour to those from exact approaches. The truncated action we use leads to overbinding of the two four-body states seen in those treatments. It also generates a third state, although only for a very narrow range of two-body scattering lengths.