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

Abstract

We determine the mass gap of a two-dimensional O(3) nonlinear sigma model augmented with a topological θ-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example θ=π 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.