蒙特卡洛方法是现代计算物理学中最早、应用最广泛的算法之一。在凝聚态物理中，这种技术最受欢迎的是Metropolis蒙卡方法。虽然Metropolis抽样方法具有很强的鲁棒性和可操作性，但它并不适用于能量和力的计算。
为了寻找一种更有效的计算方法，来自美国阿肯色大学的Laurent Bellaiche团队，在有限温度下，对具有长程相互作用的固态系统（如铁电、弛豫铁电体和多铁材料）的有效哈密顿模型进行了杂化蒙特卡洛（HMC）采样。他们探索了杂化蒙特卡罗采样方法（一种广泛用于量子电动力学的算法）在长程相互作用系统的结构预测方案方面的能力。他们的研究结果表明，在选定的模型案例中，HMC方案明显优于Metropolis蒙卡算法（MMC）和热分子动力学（MD），而且可以弥补材料科学应用中的MD。通过对面向GPU的并行化架构实现的HMC算法，可以对粒子数达到106 的体系进行大规模的HMC仿真。该算法也可用于大规模密度泛函理论计算，从而开辟更广阔的应用空间。
该文近期发表于npj Computational Materials 4: 80 (2018)，英文标题与摘要如下，原文链接：https://www.nature.com/articles/s41524-018-0137-0
Large scale hybrid Monte Carlo simulations for structure and property prediction
Sergei Prokhorenko, Kruz Kalke, Yousra Nahas & Laurent Bellaiche
The Monte Carlo method is one of the first and most widely used algorithms in modern computational physics. In condensed matter physics, the particularly popular flavor of this technique is the Metropolis Monte Carlo scheme. While being incredibly robust and easy to implement, the Metropolis sampling is not well-suited for situations where energy and force evaluations are computationally demanding. In search for a more efficient technique, we here explore the performance of Hybrid Monte Carlo sampling, an algorithm widely used in quantum electrodynamics, as a structure prediction scheme for systems with long-range interactions. Our results show that the Hybrid Monte Carlo algorithm stands out as an excellent computational scheme that can not only significantly outperform the Metropolis sampling but also complement molecular dynamics in materials science applications, while allowing ultra-large-scale simulations of systems containing millions of particles.
来源：知社学术圈
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