发表机构
Politecnico di Torino（都灵理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文介绍用于Hubbard模型的变分蒙特卡洛方法，涵盖模型、变分波函数、计算与优化，以及关联函数结果，以探测电荷、自旋有序和超导性。
AI 中文摘要
在这些讲义中，我们介绍了用于Hubbard模型的变分蒙特卡洛方法。首先，我们简要介绍单轨道Hubbard模型及其多轨道扩展，仅关注电子模型。然后，我们介绍变分蒙特卡洛工作的一般方案，并给出能够恰当描述单轨道和多轨道Hubbard模型中超导态和磁性态的变分波函数。我们还详细说明如何针对给定的波函数执行蒙特卡洛计算。我们还描述了如何利用随机重构方法优化变分波函数。最后，我们展示了一些可在变分蒙特卡洛中计算的关联函数的结果，以确定例如电荷或自旋有序以及超导性的存在。
英文摘要
In these lecture notes, we introduce the variational Monte Carlo method for the Hubbard model. First, we briefly introduce the single-orbital Hubbard model and its multi-orbital extension, focusing only on electronic models. Then, we introduce the general scheme under which variational Monte Carlo works and we present the variational wave functions that can properly describe superconductive and magnetic states in single-orbital and multi-orbital Hubbard models. We also detail how to perform Monte Carlo calculations for the given wave functions. We also describe how to optimize a variational wave function with the stochastic reconfiguration method. Finally, we present a few results for correlation functions that can be computed in variational Monte Carlo, to determine, for instance, the presence of charge or spin order and superconductivity.
Comments29 pages, 7 figures
Journal refEva Pavarini and Erik Koch (Eds.): Correlated Materials: Method and Applications, Reihe Modeling and Simulation, Vol. 16 (Forschungszentrum Jülich, 2026) http://www.cond-mat.de/events/correl26
