From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model

TL;DR

This paper introduces a sign-problem-free lattice regularization of the 1+1D O(3) nonlinear sigma model that accurately captures $ heta$ vacua and asymptotic freedom, suitable for quantum computing simulations.

Contribution

It presents the first sign-problem-free lattice model for arbitrary $ heta$ in the O(3) sigma model, enabling quantum simulations of $ heta$ vacua and generalization to CP(N-1) models.

Findings

Successfully reproduces infrared and ultraviolet physics of the model.

Demonstrates compatibility with near-term quantum devices.

Solves a longstanding sign problem in lattice gauge theories.

Abstract

Conventional lattice formulations of $\theta$ vacua in the $1+1$-dimensional $\text{O}(3)$ nonlinear sigma model suffer from a sign problem. Here, we construct the first sign-problem-free regularization for arbitrary $\theta$. Using efficient lattice Monte Carlo algorithms, we demonstrate how a Hamiltonian model of spin-$\tfrac12$ degrees of freedom on a 2-dimensional spatial lattice reproduces both the infrared sector for arbitrary $\theta$, as well as the ultraviolet physics of asymptotic freedom. Furthermore, as a model of qubits on a two-dimensional square lattice with only nearest-neighbor interactions, it is naturally suited for studying the physics of $\theta$ vacua and asymptotic freedom on near-term quantum devices. Our construction generalizes to $\theta$ vacua in all $\text{CP}(N-1)$ models, solving a long standing sign problem.