Toward a quantum simulation of nonlinear sigma models with a topological term

Abstract

We determine the mass gap of a two-dimensional $\text{O}(3)$ nonlinear sigma model augmented with a topological $\ensuremath{\theta}$-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example $\ensuremath{\theta}=\ensuremath{\pi}$ and study its critical behavior on a quantum simulator by examining the entanglement entropy of the ground state. We confirm that the quantum theory is massless in the strong-coupling regime, in agreement with analytical results. However, we also highlight the limitations of current quantum algorithms, designed for noisy intermediate-scale quantum devices, in the theory simulation at weak coupling. Finally, we compare the performance of our quantum algorithms to classical tensor network methods.