标题： 使用径向更新的完全遍历模拟 显示英文标题

标题： Fully ergodic simulations using radial updates

摘要： 混合蒙特卡洛（HMC）方法的一个合理应用常常受到大甚至无穷大的势垒的阻碍。 这些势垒将构型空间分割成不同的区域，并可能导致遍历性破坏，从而导致测量偏差。 在这项工作中，我们通过在所谓的场的“径向方向”上引入乘法Metropolis-Hastings更新来解决这个问题，这使得跨越势垒成为可能，并确保采样算法的遍历性，且计算成本相对较低。 我们在一个简单的玩具模型上演示了该算法，并展示了如何将其应用于费米子Hubbard模型，该模型描述了从可精确求解的两站点系统到$C_{20}H_{12}$全苯分子的物理现象。 我们的数值结果显示，径向更新成功消除了遍历性破坏，同时减少了自相关时间。 显示英文摘要

摘要： A sensible application of the Hybrid Monte Carlo (HMC) method is often hindered by the presence of large - or even infinite - potential barriers. These potential barriers separate the configuration space into distinct sectors and can lead to ergodicity violations that bias measurements. In this work, we address this problem by augmenting HMC with a multiplicative Metropolis-Hastings update in a so-called ''radial direction'' of the fields which enables crossing the potential barriers and ensures ergodicity of the sampling algorithm at comparably low computational cost. We demonstrate the algorithm on a simple toy model and show how it can be applied to the fermionic Hubbard model describing physics ranging from an exactly-solvable two-site system to the $C_{20}H_{12}$ perylene molecule. Our numerical results show that the radial updates successfully remove ergodicity violations, while simultaneously reducing autocorrelation times.