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

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Computational Physics

Background:

• The fermion sign problem hinders numerical simulations of quantum many-body systems.
• Quantum criticality and associated phases are difficult to study due to computational limitations.

Purpose of the Study:

• To introduce a novel framework to circumvent the fermion sign problem.
• To enable accurate numerical studies of quantum criticality and phases in problematic systems.

Main Methods:

• Leveraging imaginary-time nonequilibrium critical dynamics.
• Analyzing short-time relaxation dynamics manageable by quantum Monte Carlo simulations.
• Validating the approach on benchmark fermionic models and the Hubbard model.

Main Results:

• Accurate determination of critical properties from short-time relaxation.
• First numerically exact characterization of the Hubbard model's quantum phase diagram.
• Discovery of a continuous transition between Dirac semimetal and SU(3)-antiferromagnetic phases.

Conclusions:

• The new framework effectively bypasses the fermion sign problem for quantum criticality studies.
• The identified transition belongs to an unconventional Gross-Neveu universality class.
• This work offers a powerful tool for investigating sign-problematic systems and advancing understanding of quantum criticality.