  As an intrinsically-unbiased approach, 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 becomes less severe for larger system sizes and
eventually disappears in the thermodynamic limit, which we dub as "asymptotic
sign free". We demonstrate asymptotically-free sign in determinant QMC for
various interacting models. Moreover, based on renormalization-group-like ideas
we propose a heuristic understanding of the feature of asymptotic sign free. We
believe that asymptotic sign free behavior could shed new lights to deepening
our understanding of sign problem. More importantly, it can provide a promising
way to decipher intriguing physics in correlated models which were
conventionally thought not accessible by QMC.
