Mitigating the fermion sign problem by automatic differentiation

As an intrinsically unbiased method, the quantum Monte Carlo (QMC) method is of unique importance in simulating interacting systems. Although QMC often suffers from notorious sign problem, problem models may be mitigated by finding better choices simulation scheme. However, a general framework for identifying optimal schemes has been lacking. Here, we propose using automatic differentiation to automatically search best scheme within given ansatz Hubbard-Stratonovich transformation, which call "automatic differentiable optimization" (ADSO). We apply ADSO honeycomb lattice Hubbard model with Rashba spin-orbit coupling and demonstrate that remarkably effective mitigating even solving its problem. Specifically, finds sign-free point was previously thought sign-problematic. For discovered ADSO, ground state shown simulations possess spiral magnetic ordering; also obtained critical exponents characterizing phase transition.