Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time

TL;DR

This paper introduces a novel imaginary-time nonequilibrium approach to bypass the fermion sign problem, enabling accurate study of quantum criticality and phase transitions in challenging fermionic models.

Contribution

The authors develop a new framework that avoids the fermion sign problem in quantum Monte Carlo simulations by using short-time relaxation dynamics to study quantum criticality.

Findings

Validated approach on benchmark models

First numerically exact phase diagram of Hubbard model with SU(3) fermions

Discovered a new universality class for the Dirac semi-metal to antiferromagnetic transition

Abstract

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 a framework that circumvents the sign problem in the studies of quantum criticality and its 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 SU(3) antiferromagnetic phase. This transition defines an unconventional Gross-Neveu universality class that fundamentally reshapes current understanding of Gross-Neveu criticality. Our work provides a powerful tool for investigating sign-problematic systems and quantum criticality.