Schwinger Model with a Dynamical Axion

TL;DR

This paper demonstrates how a dynamical axion field can resolve the strong CP problem in a lattice gauge theory by showing the axion's role in relaxing the effective theta angle to zero, with results accessible on quantum hardware.

Contribution

It provides a nonperturbative lattice gauge theory simulation of axion dynamics, illustrating the relaxation of the theta angle and the axion's mass extraction using matrix product states.

Findings

Axion dynamically relaxes theta to zero in the model.

Ground-state energy becomes independent of theta.

Extracted axion mass from susceptibility and spectrum.

Abstract

One of the major open puzzles in the Standard Model of particle physics is the strong CP problem: although Quantum Chromodynamics allows a CP-violating topological $\theta$-term, experiments constrain its value to be extremely small. The Peccei--Quinn mechanism resolves this problem by promoting the $\theta$-angle to a dynamical field-introducing the axion -- whose dynamics relax the effective angle $\theta_\text{eff}$ to a CP-conserving minimum. Here, we investigate the resulting axion physics in a Hamiltonian lattice gauge theory (LGT) by coupling a quantized axion field to the massive Schwinger model with a topological $\theta$-term. Using infinite matrix product state techniques, we compute the ground-state properties of the resulting theory and demonstrate that the axion dynamically relaxes $\theta_\text{eff}$ to the minimum of the vacuum energy. Consequently, the ground-state energy becomes independent of $\theta$, demonstrating the axion-mediated solution to the strong CP problem within a fully dynamical LGT. We further analyze CP restoration and extract the axion mass from the topological susceptibility and excitation spectrum. Our results provide a nonperturbative demonstration of axion dynamics in a quantum LGT amenable to investigation on modern quantum hardware.