Cohen-Stead Benjamin, Bradley Owen, Miles Cole, Batrouni George, Scalettar Richard, Barros Kipton
Department of Physics, University of California, Davis, California 95616, USA.
Department of Physics, Cornell University, Ithaca, New York 14853, USA.
Phys Rev E. 2022 Jun;105(6-2):065302. doi: 10.1103/PhysRevE.105.065302.
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and we report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but it incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. These methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.
我们介绍了用于电子 - 声子模型的高度可扩展量子蒙特卡罗模拟的方法，并报告了正方晶格上霍斯坦模型的基准测试结果。行列式量子蒙特卡罗（DQMC）方法是在有限温度下模拟简单电子 - 声子模型的广泛使用的工具，但它的计算成本与系统大小呈立方比例增长。或者，使用混合蒙特卡罗（HMC）方法和费米子行列式的积分表示可以实现与系统大小接近线性的比例缩放。在这里，我们介绍了一系列使此类模拟更快的方法。为了应对由玻色子作用引起的“刚性”，我们回顾了傅里叶加速如何与时间步长分裂相结合。为了克服与强束缚双极化子形成相关的声子采样障碍，我们设计了近似尊重粒子 - 空穴对称性的全局蒙特卡罗更新。为了加速迭代线性求解器，我们引入了一种在无限原子质量的绝热极限下变得精确的预处理器。最后，我们展示了如何使用快速傅里叶变换加速随机测量。这些方法都是互补的，结合起来可能会根据模型细节产生多个数量级的加速。
