Renormalization of the vacuum angle in quantum mechanics, Berry phase and continuous measurements

TL;DR

This paper investigates how the vacuum angle in a quantum ring model is renormalized through various RG procedures, linking it to observable Berry phases and measurement effects, with implications for quantum Hall-like phenomena.

Contribution

It introduces a toy model demonstrating the renormalization of the vacuum angle and connects it to measurable Berry phases and measurement accuracy effects.

Findings

RG procedures yield a universal flow diagram similar to quantum Hall effect

Renormalized vacuum angle can be observed via finite measurement accuracy

Berry phase associated with slow rotation relates to the renormalized vacuum angle

Abstract

The vacuum angle $\theta$ renormalization is studied for a toy model of a quantum particle moving around a ring, threaded by a magnetic flux $\theta$. Different renormalization group (RG) procedures lead to the same generic RG flow diagram, similar to that of the quantum Hall effect. We argue that the renormalized value of the vacuum angle may be observed if the particle's position is measured with finite accuracy or coupled to additional slow variable, which can be viewed as a coordinate of a second (heavy) particle on the ring. In this case the renormalized $\theta$ appears as a magnetic flux this heavy particle sees, or the Berry phase, associated with its slow rotation.