论文标题
$θ$真空的晶格正规化：异常和Qubit模型
Lattice regularizations of $θ$ vacua: Anomalies and qubit models
论文作者
论文摘要
异常是一种有力的方法，可以深入了解量子场理论可能的晶格正规化。在这项工作中，我们认为给定对称性的连续异常可以与显然对称的局部，局部的晶格正规化相匹配，仅在（i）（i）对称性动作是异地的，或（ii）如果连续脉管在lattice上精确地重现了连续性异常。我们考虑了QCD的一类原型模型的晶格正规化：（1+1） - 差异无渐近的Grassmannian非线性Sigma Sigma模型（NLSMS），具有$θ$项。使用格拉斯曼尼亚NLSM作为案例研究，我们提供了实现两种可能性的晶格正规化示例。为了可能（i），我们认为可以从$ \ mathrm {su}（n）$ antiferromagnets获得具有明确定义的连续限制的grassmannian nlsms，从而再现了$θ$ vacua的红外物理学和紫外线物理学的紫外线物理。这些结果使新的经典算法在对这些量子场理论的晶格蒙特卡洛研究中的应用，并提供适合其量子模拟的可行实现。另一方面，我们表明，令人惊讶的是，由于Berg和Lüscher而导致的$θ$ Vacua的常规晶格正规化恰好在晶格上复制了异常，从而实现了第二种可能性。
Anomalies are a powerful way to gain insight into possible lattice regularizations of a quantum field theory. In this work, we argue that the continuum anomaly for a given symmetry can be matched by a manifestly-symmetric, local, lattice regularization in the same spacetime dimensionality only if (i) the symmetry action is offsite, or (ii) if the continuum anomaly is reproduced exactly on the lattice. We consider lattice regularizations of a class of prototype models of QCD: the (1+1)-dimensional asymptotically-free Grassmannian nonlinear sigma models (NLSMs) with a $θ$ term. Using the Grassmannian NLSMs as a case study, we provide examples of lattice regularizations in which both possibilities are realized. For possibility (i), we argue that Grassmannian NLSMs can be obtained from $\mathrm{SU}(N)$ antiferromagnets with a well-defined continuum limit, reproducing both the infrared physics of $θ$ vacua and the ultraviolet physics of asymptotic freedom. These results enable the application of new classical algorithms to lattice Monte Carlo studies of these quantum field theories, and provide a viable realization suited for their quantum simulation. On the other hand, we show that, perhaps surprisingly, the conventional lattice regularization of $θ$ vacua due to Berg and Lüscher reproduces the anomaly exactly on the lattice, providing a realization of the second possibility.
