Limit Cycles from the Similarity Renormalization Group

TL;DR

This paper explores the presence of limit cycles in the similarity renormalization group (SRG) framework, proposing a method to detect and analyze their periodicity, with applications demonstrated on the inverse square potential.

Contribution

It introduces a quantitative approach to identify and measure limit cycles in SRG-evolved interactions, comparing different SRG generators for effectiveness.

Findings

Limit cycles can be detected in SRG-evolved interactions.

A method to extract the period of limit cycles is developed.

The inverse square potential exhibits a clear limit cycle behavior.

Abstract

We investigate renormalization group limit cycles within the similarity renormalization group (SRG) and discuss their signatures in the evolved interaction. A quantitative method to detect limit cycles in the interaction and to extract their period is proposed. Several SRG generators are compared regarding their suitability for this purpose. As a test case, we consider the limit cycle of the inverse square potential.