The auxiliary-field quantum Monte Carlo (AFMC) method is a powerful and widely used technique for ground-state and finite-temperature simulations of quantum many-body systems. We introduce several algorithmic improvements for finite-temperature AFMC calculations of dilute fermionic systems that reduce the computational complexity of most parts of the algorithm. This is principally achieved by reducing the number of single-particle states that contribute at each configuration of the auxiliary fields to a number that is of the order of the number of fermions. Our methods are applicable for both the canonical and grand-canonical ensembles. We demonstrate the reduced computational complexity of the methods for the homogeneous unitary Fermi gas.

辅助场量子蒙特卡洛（AFMC）方法是一种功能强大且广泛使用的技术，用于量子多体系统的基态和有限温度模拟。我们为稀铁离子系统的有限温度AFMC计算引入了几种算法改进，可减少算法大部分部分的计算复杂性。这主要是通过将对辅助场的每种构型有贡献的单粒子态的数量减少到与费米子数量级相同的数量来实现的。我们的方法适用于正典和大正典合奏。我们证明了均相一元费米气体方法的降低的计算复杂性。