Shi Hao, Zhang Shiwei
Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA.
J Chem Phys. 2021 Jan 14;154(2):024107. doi: 10.1063/5.0031024.
The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here, we introduce the theory and algorithm of the method specialized for real materials and present several recent developments. We give a systematic exposition of the key steps of AFQMC, closely tracking the framework of a modern software library we are developing. The building of a Monte Carlo Hamiltonian, projecting to the ground state, sampling two-body operators, phaseless approximation, and measuring ground state properties are discussed in detail. An advanced implementation for multi-determinant trial wave functions is described, which dramatically speeds up the algorithm and reduces the memory cost. We propose a self-consistent constraint for real materials, and discuss two flavors for its realization, either by coupling the AFQMC calculation to an effective independent-electron calculation or via the natural orbitals of the computed one-body density matrix.
辅助场量子蒙特卡罗（AFQMC）方法是一种用于关联多电子系统的通用数值方法，越来越多地应用于晶格模型、原子、分子和固体中。在此，我们介绍针对实际材料的该方法的理论和算法，并展示一些近期的进展。我们系统地阐述了AFQMC的关键步骤，紧密遵循我们正在开发的一个现代软件库的框架。详细讨论了构建蒙特卡罗哈密顿量、投影到基态、对两体算符进行采样、无相近似以及测量基态性质。描述了一种针对多行列式试探波函数的先进实现方式，它极大地加快了算法速度并降低了内存成本。我们为实际材料提出了一种自洽约束，并讨论了实现它的两种方式，要么通过将AFQMC计算与有效的独立电子计算耦合，要么通过计算得到的一体密度矩阵的自然轨道。
