标题： 深度学习格点规范理论 显示英文标题

标题： Deep learning lattice gauge theories

摘要： 蒙特卡罗方法已经带来了对格点规范理论强耦合行为的深刻见解，并产生了诸如重子质量的第一性原理计算等显著结果。 尽管在过去四十年中取得了巨大进展，但诸如符号问题和无法模拟实时动力学等基本挑战仍然存在。 神经网络量子态作为一种替代方法浮出水面，旨在克服这些挑战。 在本工作中，我们使用规范不变的神经网络量子态，在$2+1$维度中精确计算$\mathbb{Z}_N$格点规范理论的基态。 通过迁移学习，我们研究了这些理论的不同拓扑相和禁闭相变。 对于$\mathbb{Z}_2$，我们识别出一个连续相变并计算临界指数，发现与预期的伊辛普适类的现有数值结果高度一致。 在$\mathbb{Z}_3$的情况下，我们观察到一个弱第一阶相变并确定了临界耦合。 我们的研究结果表明，神经网络量子态是精确研究格点规范理论的一种有前景的方法。 显示英文摘要

摘要： Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.