Limit cycles of effective theories

TL;DR

This paper introduces a novel approach using similarity renormalization group procedures to analyze limit cycles in effective quantum theories, linking asymptotic freedom with bound state hierarchies.

Contribution

It presents a new method for studying renormalization group limit cycles in effective theories through similarity transformations.

Findings

Demonstrates a simple example with ultraviolet divergence and limit cycles.

Connects asymptotic freedom with a hierarchy of bound states.

Shows the effectiveness of the new analysis method.

Abstract

A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains a logarithmic ultraviolet divergence that is generated by both real and imaginary parts of the Hamiltonian matrix elements. Discussion of the example includes a connection between asymptotic freedom with one scale of bound states and the limit cycle with an entire hierarchy of bound states.