Schwinger Model with a Dynamical Axion

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.