Universal entanglement growth along imaginary time in quantum critical systems

Characterizing universal entanglement features in higher-dimensional quantum matter is a central challenge in quantum information science and condensed matter physics. While subleading corner terms in two-dimensional systems encode the essential fingerprints of the underlying conformal field theory, accessing these features remains notoriously difficult compared to the well-understood one-dimensional case. Here, we uncover a universal non-equilibrium scaling law governing imaginary-time entanglement dynamics. We demonstrate that for 2D quantum critical points, the corner entanglement grows logarithmically with imaginary time, with a coefficient dictated solely by the universality class. By validating this framework through large-scale Quantum Monte Carlo simulations, we definitively resolve the entanglement structure of the interacting Gross-Neveu-Yukawa critical point, revealing significant interaction-driven deviations from free-fermion theories. Crucially, our approach extracts high-precision universal data from the early stages of relaxation, thereby bypassing the prohibitive computational bottlenecks of full equilibrium convergence. This work establishes a direct bridge between non-equilibrium critical phenomena and entanglement spectroscopy, providing a robust theoretical blueprint for applications on both classical numerical computation and emerging quantum hardware.