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

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-$\frac{1}{2}$ 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.

7 pages, 4 figures

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• Uncovering Emergent Spacetime Supersymmetry with Rydberg Atom Arrays
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
• Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization
• Winding theta and destructive interference of instantons
• Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method
• Transverse Field $\gamma$-Matrix Spin Chains