From Asymptotic Freedom to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:math> Vacua: Qubit Embeddings of the O(3) Nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math> Model
Stephan Caspar, Hersh Singh
Abstract
Conventional lattice formulations of θ vacua in the 1+1-dimensional O(3) nonlinear sigma model suffer from a sign problem. Here, we construct the first sign-problem-free regularization for arbitrary θ. Using efficient lattice Monte Carlo algorithms, we demonstrate how a Hamiltonian model of spin-1/2 degrees of freedom on a two-dimensional spatial lattice reproduces both the infrared sector for arbitrary θ, 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 θ vacua and asymptotic freedom on near-term quantum devices. Our construction generalizes to θ vacua in all CP(N-1) models, solving a long-standing sign problem.