Universal Entanglement Growth along Imaginary Time in Quantum Critical Systems

TL;DR

This paper reveals a universal scaling law for entanglement growth in quantum critical systems along imaginary time, verified through simulations, and offers a new approach to studying entanglement in higher-dimensional quantum matter.

Contribution

It introduces a non-equilibrium scaling law for corner entanglement entropy growth in quantum critical systems and demonstrates its validity via Quantum Monte Carlo simulations.

Findings

Corner entanglement entropy grows linearly with log of imaginary time

Universal data can be extracted early in relaxation process

Scaling law applies across different quantum critical universality classes

Abstract

Characterizing universal entanglement features in higher-dimensional quantum matter is a central goal of quantum information science and condensed matter physics. While the subleading corner terms in two-dimensional quantum systems encapsulate essential universal information of the underlying conformal field theory, our understanding of these features remains remarkably limited compared to their one-dimensional counterparts. We address this challenge by investigating the entanglement dynamics of fermionic systems along the imaginary-time evolution. We uncover a pioneering non-equilibrium scaling law where the corner entanglement entropy grows linearly with the logarithm of imaginary time, dictated solely by the universality class of the quantum critical point. Through unbiased Quantum Monte Carlo simulations, we verify this scaling in the interacting Gross-Neveu-Yukawa model, demonstrating that universal data can be accurately recovered from the early stages of relaxation. Our findings significantly circumvent the computational bottlenecks inherent in reaching full equilibrium convergence. This work establishes a direct link between the fundamental theory of non-equilibrium critical phenomena and the high-precision determination of universal entanglement properties on both classical and quantum platforms, paving the way for probing the rich entanglement structure of quantum critical systems.