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arXiv · 2203.15766

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

Stephan Caspar·Hersh Singh
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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.

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Stephan Caspar, Hersh Singh. 2022-03-29. From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model. https://doi.org/10.1103/physrevlett.129.022003

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