AI 中文总结
本研究在随机级数展开框架内提出高效通用算法，可计算对角与非对角算符的虚时关联函数，经基准测试验证其精度与效率良好。
AI 中文摘要
结合数值解析延拓技术，量子蒙特卡洛（QMC）方法可从虚时关联函数中提取实频动力学性质。然而，QMC模拟高效计算虚时关联函数可能（取决于所用特定模型）存在挑战，尤其针对计算基下非对角的算符。本研究在随机级数展开（SSE）框架内提出一种高效通用算法，用于计算对角与非对角算符的虚时关联函数。该算法基于SSE算符串的离散虚时切片，在无离散误差的明确定义虚时点网格上提供关联函数。针对非对角算符，推导直接集成到现有SSE定向环或集团更新方案中的估计量，仅引入极小计算开销。在一维横场伊辛模型（采用集团更新采样）与XXZ自旋链（采用定向环采样）上对该方法进行基准测试，其结果与小系统的精确对角化结果吻合极佳（仅存在统计误差），还对更大系统进行研究以验证其效率。
英文摘要
Combined with numerical analytic continuation techniques, quantum Monte Carlo (QMC) methods enable the extraction of real-frequency dynamical properties from imaginary-time correlation functions. However, the efficient computation of imaginary-time correlation functions by QMC simulations can (depending on the particular model used) be challenging, particularly for operators that are off-diagonal in the computational basis. In this work, we present an efficient and general algorithm within the stochastic series expansion (SSE) framework for evaluating imaginary-time correlation functions of both diagonal and off-diagonal operators. The algorithm builds on a discrete imaginary-time slicing of the SSE operator string, which provides correlation functions on a grid of well-defined imaginary-time points with no discretization error. For off-diagonal operators, we derive estimators that integrate directly into the existing SSE directed-loop or cluster updating schemes, introducing only minimal computational overhead. We benchmark the method on the one-dimensional transverse-field Ising model (sampling with cluster updates) and XXZ spin chain (using directed-loop sampling), demonstrating excellent agreement (with only statistical errors) with exact diagonalization of small systems. We also study larger systems to demonstrate efficiency.
Comments19 pages, 10 figures
