Onset of the Limit Cycle and Universal Three-Body Parameter in Efimov Physics

TL;DR

This paper demonstrates that the onset of the Efimov limit cycle and the three-body parameter are universal features in Efimov physics, independent of short-range details, using an exact functional renormalization-group approach.

Contribution

It provides a theoretical demonstration of the universality of the limit cycle onset and the three-body parameter in Efimov physics through a novel RG analysis.

Findings

The flow into the limit cycle is universal across different potentials.

The three-body parameter measured in effective range units is universal.

A topological connection between the limit cycle and few-body physics is established.

Abstract

The Efimov effect is the only experimentally realized universal phenomenon that exhibits the renormalization-group limit cycle with the three-body parameter parametrizing a family of universality classes. Recent experiments in ultracold atoms have unexpectedly revealed that the three-body parameter itself is universal when measured in units of an effective range. By performing an exact functional renormalization-group analysis with various finite-range interaction potentials, we demonstrate that the onset of the renormalization-group flow into the limit cycle is universal, regardless of short-range details, which connects the missing link between the two universalities of the Efimov physics. A close connection between the topological property of the limit cycle and few-body physics is also delineated.