Asymptotic sign free in interacting fermion models

As an intrinsically-unbiased method, quantum Monte Carlo (QMC) is of vital importance in understanding correlated phases of matter. Unfortunately, it often suffers notorious sign problem when simulating interacting fermion models. Here, we show for the first time that there exist interacting fermion models whose sign problem are less severe for larger system sizes and eventually disappears in the thermodynamic limit, which we dub as ``asymptotic sign free'' (ASF). We demonstrate asymptotically-free sign for various interacting models featuring Dirac fermions by determinant QMC. The numerical results offer unambiguous examples showing the asymptotically free behavior of sign problem in different models. Moreover, based on renormalization group ideas we propose an heuristic understanding of this novel feature of asymptotic sign-free. We believe that the asymptotic sign free behavior will shed new lights on deeper understanding of sign problem, and more importantly, applying QMC to deciphering quantum many-body physics in broader strongly correlated systems.