Imaginary-time Evolution Demonstrates Universal Entanglement in Fermionic Quantum Systems

Understanding how entanglement grows in complex materials represents a fundamental challenge in modern physics, and researchers are now shedding new light on this process. Chang-Yu Shen, Shuai Yin, and Zi-Xiang Li, from the Beijing National Laboratory for Condensed Matter Physics, investigate entanglement dynamics in systems undergoing quantum phase transitions, focusing on how entanglement evolves over imaginary time. Their work reveals a novel principle, demonstrating that entanglement increases linearly with the logarithm of imaginary time, and this growth is determined only by the system’s underlying properties, not specific details of its composition. This discovery circumvents the need for computationally intensive calculations of full equilibrium states, allowing scientists to accurately measure universal characteristics from the very beginning of a system’s relaxation, and ultimately offers a new pathway to explore the intricate entanglement structures within critical systems.

This discovery circumvents the need for computationally intensive calculations of full equilibrium states, allowing scientists to accurately measure universal characteristics from the very beginning of a system’s relaxation, and ultimately offers a new pathway to explore the intricate entanglement structures within critical systems.

Entanglement Dynamics via Imaginary Time Monte Carlo

Scientists pioneered a novel approach to characterize universal entanglement features in two-dimensional systems, focusing on the dynamics of fermionic systems evolving in imaginary time, a cornerstone of computational many-body physics. The study addresses a long-standing challenge in condensed matter physics, namely the difficulty in accurately determining subleading corner terms in entanglement entropy, which are often obscured by non-universal area-law contributions and require computationally intensive calculations.

Researchers employed unbiased Monte Carlo simulations to investigate entanglement dynamics, circumventing the need for full equilibrium convergence and significantly reducing computational bottlenecks. The core of the work involves examining how entanglement entropy changes over imaginary time, a technique used to project towards ground states from arbitrary initial configurations, and increasingly relevant with the development of quantum computers. Experiments employ a precise measurement of the corner entanglement entropy, revealing a previously unknown non-equilibrium scaling law, where the entropy grows linearly with the logarithm of imaginary time.

This scaling is dictated solely by the universality class of the critical point, demonstrating a fundamental connection between non-equilibrium critical phenomena and the determination of universal entanglement properties. To validate this scaling, the team performed systematic simulations of free Dirac fermions, recovering a coefficient consistent with established equilibrium results, and then extended the method to the interacting Gross-Neveu-Yukawa model and the antiferromagnetic phase. The technique achieves high precision in extracting universal data even during the early stages of relaxation, bypassing the substantial computational demands of traditional equilibrium methods.

This innovative protocol delivers a robust framework for probing universal entanglement properties in the short-time regime, offering a viable route to enhance the efficiency of quantum algorithms requiring ground-state preparation on diverse quantum platforms and enriching the fundamental theory of non-equilibrium criticality. The results demonstrate that the corner contribution to entanglement entropy follows a universal logarithmic scaling with evolution time, governed by a size-independent coefficient dictated by the underlying conformal field theory.

Logarithmic Growth of Corner Entanglement Entropy

Scientists have achieved a breakthrough in understanding entanglement, a fundamental quantum phenomenon, in complex materials. Their work focuses on characterizing universal entanglement features in two-dimensional systems, specifically examining how entanglement evolves over imaginary time. The team investigated the dynamics of fermionic systems, uncovering a novel non-equilibrium scaling law where the corner entanglement entropy grows linearly with the logarithm of imaginary time.

This growth is dictated solely by the universality class of the critical point, meaning the specific microscopic details of the material are irrelevant to this fundamental behavior. Through extensive, unbiased Monte Carlo simulations, researchers verified this scaling law using the interacting Gross-Neveu-Yukawa model. The simulations demonstrate that universal data, representing core properties of the material, can be accurately recovered even during the early stages of relaxation, significantly reducing the computational demands traditionally required to reach full equilibrium.

Measurements confirm that the corner contribution to entanglement entropy follows a universal logarithmic scaling with evolution time, governed by a size-independent coefficient. Experiments revealed a consistent coefficient of 0.3116 for free Dirac fermions, aligning with previously established equilibrium results. Crucially, the team demonstrated the versatility of this approach by successfully extracting universal data within the antiferromagnetic phase using sign-free quantum Monte Carlo methods. Analysis of the data shows that the corner entanglement entropy scales with the logarithm of imaginary time, exhibiting a “size-independent plateau” determined solely by the time elapsed.

Further measurements, conducted across system sizes ranging from L=6 to L=54, consistently yielded a coefficient of 0.3111, confirming the robustness of the observed scaling behavior. This work establishes a new framework for probing universal entanglement properties in the short-time regime, offering a highly efficient numerical protocol for entanglement spectroscopy and potentially enhancing quantum algorithms.

Entanglement Growth Reveals Universal Scaling Law

This research establishes a new understanding of entanglement growth in two-dimensional quantum systems nearing a critical point, revealing a previously unobserved scaling law governing how entanglement entropy evolves over imaginary time. Scientists demonstrated that the change in corner entanglement entropy increases linearly with the logarithm of imaginary time, a relationship determined solely by the system’s underlying universality class, and independent of system size during early relaxation stages.

This finding circumvents the substantial computational demands typically associated with simulating systems until they reach full equilibrium. The team validated this scaling through Monte Carlo simulations of an interacting model, successfully extracting universal data from the system’s initial relaxation phase, and determining a universal coefficient for the corner entanglement contribution. Importantly, the results for this model demonstrate a significantly enhanced corner contribution compared to non-interacting systems, highlighting the impact of interactions on entanglement.

While acknowledging that calculations are limited to short imaginary times due to computational constraints, the authors suggest this approach offers a pathway to study systems where the ‘sign problem’ severely hinders traditional methods. Future work may extend this framework to explore more complex quantum systems, including deconfined quantum critical points and Dirac spin liquids, and offers a route for direct experimental verification using current quantum computing hardware.