从头计算辅助场量子蒙特卡洛方法在热力学极限下的应用
Ab Initio Auxiliary-Field Quantum Monte Carlo in the Thermodynamic Limit
AI总结：
本文提出一种基于张量超收缩与k点对称性的从头计算辅助场量子蒙特卡洛方法，实现对固体的热力学极限和完整基组极限的高效计算，为预测性固体模拟提供了一种新的通用方法。
摘要：
从头计算辅助场量子蒙特卡洛（AFQMC）是一种可以系统性改进的多体方法，但其在扩展固体中的应用受到不利的计算规模和内存需求的严重限制，这些限制阻碍了直接访问热力学极限和完整基组极限。通过结合张量超收缩与k点对称性，我们将从头计算AFQMC在固体中的计算和内存规模分别减少到O(N³)和O(N²)，与扩散蒙特卡洛方法相当。这使得能够在绝缘体、金属和强相关固体中同时进行热力学极限和完整基组AFQMC计算，而无需嵌套、局部近似、经验有限尺寸修正或复合方案。我们的结果确立了AFQMC作为一种通用的、可以系统性改进的替代方法，用于预测性从头计算固体模拟，能够在统一框架中获得准确的能量和磁学可观测量。
英文摘要：
Ab initio auxiliary-field quantum Monte Carlo (AFQMC) is a systematically improvable many-body method, but its application to extended solids has been severely limited by unfavorable computational scaling and memory requirements that obstruct direct access to the thermodynamic and complete-basis-set limits. By combining tensor hypercontraction with $\mathbf{k}$-point symmetry, we reduce the computational and memory scaling of ab initio AFQMC for solids to $\mathcal O(N^3)$ and $\mathcal O(N^2)$, respectively, with an arbitrary basis, comparable to diffusion Monte Carlo. This enables direct and simultaneous thermodynamic-limit and complete-basis-set AFQMC calculations across insulating, metallic, and strongly correlated solids, without embedding, local approximations, empirical finite-size corrections, or composite schemes. Our results establish AFQMC as a general-purpose, systematically improvable alternative to diffusion Monte Carlo and coupled-cluster methods for predictive ab initio simulations of solids, enabling accurate energies and magnetic observables within a unified framework.
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