论文标题
从渐近自由到$θ$ vacua：o（3）非线性$σ$型号的量子嵌入
From asymptotic freedom to $θ$ vacua: Qubit embeddings of the O(3) nonlinear $σ$ model
论文作者
论文摘要
$ 1+1 $ -Dimensional $ \ text {o}（3）$ nonlinear Sigma模型的常规晶格配方$θ$ vacua遇到了符号问题。在这里，我们为任意$θ$构建了第一个无标志的正规化。使用有效的晶格蒙特卡洛算法，我们演示了旋转的哈密顿模型如何 - $ \ tfrac12 $自由度在二维空间晶格上重现了任意$θ$的红外扇形，以及差异性自由的紫外物理学。此外，作为二维方晶格的Qubits模型，它仅与最近的邻居相互作用，它自然适合研究$θ$ vacua的物理和近期量子设备上的渐近自由。我们的构造在所有$ \ text {cp}（n-1）$型号中概括为$θ$ vacua，解决了一个长期的标志问题。
Conventional lattice formulations of $θ$ 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 $θ$. 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 $θ$, 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 $\text{CP}(N-1)$ models, solving a long standing sign problem.
