Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term

TL;DR

This paper explores quantum algorithms to simulate a 2D nonlinear sigma model with a topological term, analyzing its mass gap and critical behavior, and compares quantum and classical methods.

Contribution

It demonstrates the use of tensor networks and digital quantum algorithms to study the model's mass gap and criticality, highlighting current limitations and performance comparisons.

Findings

Quantum algorithms confirm massless behavior at strong coupling.

Limitations of current quantum algorithms at weak coupling.

Quantum algorithms show competitive performance with classical methods.

Abstract

We determine the mass gap of a two-dimensional $O(3)$ nonlinear sigma model augmented with a topological $\theta$-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example $\theta = \pi$ and study its critical behaviour 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.