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.