In this talk, I will present two recent developments in the application of quantum Monte
Carlo (QMC) methods to strongly correlated fermionic systems. First, we explore
imaginary-time non-equilibrium dynamics in the context of Dirac-fermion quantum
criticality. By utilizing non-equilibrium quantum critical scaling in the short-time regime, we
propose a novel framework to extract quantum critical properties even in models severely
restricted by the fermion sign problem. Applying this framework to the SU(3) repulsive
Hubbard model, we identify an antiferromagnetic (AFM) quantum critical point belonging
to a new Gross-Neveu universality class. In the second part, we use QMC to investigate
the non-Hermitian Hubbard model on the honeycomb lattice featuring non-reciprocal
hopping. Our results reveal that AFM order is surprisingly enhanced by the non-
Hermitian, non-reciprocal hopping. Furthermore, we demonstrate that at the quantum
critical point separating the Dirac semimetal and the AFM phase, Hermiticity is emergent,
and the transition belongs to the Hermitian chiral XY Gross-Neveu universality class.

References:
1. Yin-Kai Yu, Zhi-Xuan Li, Shuai Yin, Zi-Xiang Li, Science Advances 12,eadz4856 (2026)
2. Yin-Kai Yu, Zhi Zeng, Yu-Rong Shu, Zi-Xiang Li, Shuai Yin, Phys. Rev. Lett. 136, 086502 (2026)
3. Chang-Yu Shen, Shuai Yin and Zi-Xiang Li, arXiv:2512.23361 (2025)
4. Xue-Jia Yu, Zhiming Pan, Limei Xu, Zi-Xiang Li, Phys. Rev. Lett. 132, 116503 (2024).

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