机器学习得到的经典完美定点作用量下的HMC与梯度流
HMC and gradient flow with machine-learned classically perfect fixed-point actions
AI总结：
该研究针对四维SU(3)规范理论，用格点规范协变卷积神经网络参数化经典完美的定点格点作用量，实现更优参数化并展示其HMC高效模拟，还论证其可定义树图级无伪影梯度流并给出标度初步结果。
摘要：
定点（FP）格点作用量具有经典完美性，即其连续经典性质不受离散化效应影响，且弱耦合下格点伪影有望被抑制。因此，它们为用更粗格点提取连续物理提供了可能途径，可规避连续极限下临界慢化与拓扑冻结问题。我们利用机器学习方法，通过格点规范协变卷积神经网络为四维SU(3)规范理论参数化FP作用量。大算子空间使我们找到比先前研究更优的参数化形式，并展示如何用混合蒙特卡洛（HMC）算法高效模拟此类作用量。此外，我们论证FP格点作用量可用于定义树图级无格点伪影的经典完美梯度流，并给出FP作用量下梯度流标度的初步结果。
英文摘要：
Fixed-point (FP) lattice actions are classically perfect, i.e., they have continuum classical properties unaffected by discretization effects and are expected to have suppressed lattice artifacts at weak coupling. Therefore they provide a possible way to extract continuum physics with coarser lattices, allowing to circumvent problems with critical slowing down and topological freezing towards the continuum limit. We use machine-learning methods to parameterize a FP action for four-dimensional SU(3) gauge theory using lattice gauge-covariant convolutional neural networks. The large operator space allows us to find superior parameterizations compared to previous studies and we show how such actions can be efficiently simulated with the Hybrid Monte Carlo algorithm. Furthermore, we argue that FP lattice actions can be used to define a classically perfect gradient flow without any lattice artifacts at tree level. We present initial results for scaling of the gradient flow with the FP action.
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