Renormalization Group Limit Cycles in Quantum Mechanical Problems

TL;DR

This paper develops a renormalization group framework for two-body quantum problems, revealing limit cycles that produce a scaling spectrum, with implications for Efimov physics.

Contribution

It introduces a RG approach that uncovers limit cycles in two-body interactions approaching inverse square laws, explaining scaling phenomena in quantum spectra.

Findings

Limit cycles emerge in RG flow for inverse square interactions.

Scaling structures appear in the energy spectrum due to these cycles.

Relevance to Efimov physics in nuclear systems.

Abstract

We formulate a renormalization group (RG) for the interaction parameters of the general two-body problem and show how a limit cycle emerges in the RG flow if the interaction approaches an inverse square law. This limit cycle generates a scaling structure in the energy spectrum. Our demonstration is relevant to the Efimov problem in nuclear physics where similar scaling appears.