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

• URL: http://arxiv.org/abs/2203.15766v1
• Date: Tue, 29 Mar 2022 17:23:47 GMT
• Title: From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model
• Authors: Stephan Caspar, Hersh Singh
• Abstract summary: We construct the first sign-problem-free regularization for arbitrary $theta$ using efficient lattice Monte Carlo algorithms. Our constructions generalize to $theta$ vacua in all $textCP(N-1)$ models, solving a long standing sign problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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