Lattice techniques to investigate the strong $CP$ problem: lessons from a toy model

TL;DR

This paper explores lattice techniques using a quantum mechanical rotor as a toy model to understand the strong $CP$ problem, addressing issues like topology freezing and the sign problem relevant to lattice QCD.

Contribution

It introduces a simplified quantum rotor model to investigate lattice methods for the strong $CP$ problem, providing insights applicable to more complex QCD simulations.

Findings

The quantum rotor model exhibits similar topological challenges as lattice QCD.

Proposed lattice techniques can mitigate topology freezing in the toy model.

Insights gained may inform future lattice QCD studies on the strong $CP$ problem.

Abstract

Recent studies have claimed that the strong $CP$ problem does not occur in QCD, proposing a new order of limits in volume and topological sectors when studying observables on the lattice. We study the effect of the topological term on a simple quantum mechanical rotor that allows a lattice description. We particularly focus on recent proposals to face the challenging problems that this study poses in lattice QCD and that are also present in the quantum rotor, such as topology freezing and the sign problem.