标题： 虚构粒子 Hubbard 模型的量子路径积分方法 显示英文标题

标题： Quantum Path-integral Method for Fictitious Particle Hubbard Model

摘要： 我们提出了一种路径积分蒙特卡罗算法，用于模拟由广义交换统计规律支配的虚构粒子的格点系统。 该方法最初是为连续系统提出的，在配分函数中引入了一个连续参数$\xi$，该参数在玻色子（$\xi = 1$）和费米子（$\xi = -1$）统计之间进行插值。 我们将这种方法推广到离散格点模型，并将其应用于二维虚构粒子的哈伯德模型，包括玻色-哈伯德模型和费米-哈伯德模型作为特殊情况。 通过结合重加权和$\xi$外推技术，我们能够访问半满和掺杂区域。 特别是，我们证明了即使在强关联的掺杂系统中，该方法仍然有效，而在这种系统中费米子符号问题会阻碍传统的量子蒙特卡罗方法。 我们的结果验证了虚构粒子框架在格点模型中的适用性，并确立了它作为强相互作用费米系统中符号问题缓解的一种有前景的工具。 显示英文摘要

摘要： We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a continuous parameter $\xi$ in the partition function that interpolates between bosonic ($\xi = 1$) and fermionic ($\xi = -1$) statistics. We generalize this approach to discrete lattice models and apply it to the two-dimensional Hubbard model of fictitious particles, including the Bose- and Fermi-Hubbard models as special cases. By combining reweighting and $\xi$-extrapolation techniques, we access both half-filled and doped regimes. In particular, we demonstrate that the method remains effective even in strongly correlated, doped systems where the fermion sign problem hinders conventional quantum Monte Carlo approaches. Our results validate the applicability of the fictitious particle framework on lattice models and establish it as a promising tool for sign-problem mitigation in strongly interacting fermionic systems.