Preempting fermion sign problem: Unveiling quantum criticality through nonequilibrium dynamics in imaginary time

The notorious fermion sign problem, arising from fermion statistics, presents a fundamental obstacle to the numerical simulation of quantum many-body systems. Here, we introduce an innovative framework that circumvents the sign problem in the studies of quantum criticality and the associated phases by leveraging imaginary-time nonequilibrium critical dynamics. We demonstrate that the critical properties can be accurately determined from the system’s short-time relaxation, a regime where the sign problem remains manageable for quantum Monte-Carlo (QMC) simulations. After validating this approach on two benchmark fermionic models, we apply it to the sign-problematic Hubbard model hosting SU(3)-symmetric Dirac fermions. We present the first numerically exact characterization of its quantum phase diagram, revealing a continuous transition between a Dirac semi-metal and a novel antiferromagnetic phase, which belongs to a new universality class, distinct from the previously known Gross-Neveu transitions. Our work provides a powerful tool for investigating sign-problematic systems and quantum criticality.