Efimov effect from functional renormalization

TL;DR

This paper uses a functional renormalization group approach to study Efimov physics in few-body non-relativistic atomic systems near a Feshbach resonance, revealing limit cycle behavior and calculating Efimov parameters.

Contribution

It applies a field-theoretic FRG method to analyze Efimov states across different atomic systems, providing new insights into their scale invariance and limit cycle scaling behaviors.

Findings

Exact two-body solutions match unitary fixed point behavior.

Three-body solutions exhibit Efimov limit cycle scaling.

Efimov parameter approximately 1.006 for relevant systems.

Abstract

We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component fermions with U(1)\times SU(2) symmetry and three-component fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant unitarity limit for infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed point behavior for all considered systems. Nevertheless, the numerical three-body solution in the s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be approximately s=1.006, consistent with the result of Efimov.