We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by 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 in strongly correlated, doped systems, offering a distinct advantage by naturally operating in the canonical ensemble. Our results validate the applicability of the fictitious-particle framework to lattice models and establish it as a promising, complementary tool for investigating strongly interacting fermionic systems.

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• Magnetism
• Quantum statistical mechanics
• Mott insulators
• Hubbard model
• Path-integral Monte Carlo