Renormalization of the vacuum angle for a particle on a ring

TL;DR

This paper investigates how the vacuum angle in a quantum particle on a ring model undergoes renormalization, revealing a flow similar to the Quantum Hall effect through exact RG equations.

Contribution

It introduces an exact RG framework for analyzing the topological vacuum angle in a quantum mechanical system, linking it to topological charge loss.

Findings

RG flow diagram resembles Quantum Hall effect

Renormalization linked to loss of topological information

Exact RG equations derived for the model

Abstract

We analyze the vacuum (topological) angle $\theta$ renormalization for the quantum mechanical model of a particle moving around a ring, where $\theta$ is the magnetic flux through the ring. We construct a renormalization group (RG) transformation for this model and derive exact RG equations which lead to the flow diagram similar to that of the Quantum Hall effect. Renormalization of $\theta$ is seen to follow from the loss of information about the initial topological charge in the course of the RG procedure.