Researchers Discover Universal Short-Time Channel Wave Structure in Symmetry-Resolved Dynamics

The behaviour of quantum systems following a sudden disturbance, known as a ‘quantum quench’, reveals fundamental insights into how entanglement, a key feature of quantum mechanics, evolves over time, and researchers are now discovering surprisingly consistent patterns in this process. Lihui Pan, Jie Chen, and Chun Chen from Shanghai Jiao Tong University, along with Xiaoqun Wang from Zhejiang University and Nanjing University, demonstrate the emergence of a universal short-time structure in these dynamics, termed the ‘entanglement channel wave’. This wave appears consistently across diverse quantum systems, including fermions and bosons with or without interactions and disorder, suggesting its independence from specific material properties, and offering a new lens through which to understand the complex growth of entanglement following a quantum quench. The discovery provides a powerful framework for predicting and controlling entanglement in a wide range of quantum technologies, and deepens our understanding of fundamental quantum behaviour.

Symmetry-Resolved Entanglement in Quench Dynamics

This research investigates symmetry-resolved entanglement (SRE) in various quantum many-body systems, focusing on how entanglement changes after a sudden disturbance, known as a quantum quench. The authors use advanced numerical techniques, including the Krylov subspace method, to calculate SRE in different systems. A central theme is understanding how SRE differs from standard entanglement measures and how it reveals information about the underlying physics, particularly in the presence of symmetry and disorder. The research demonstrates that SRE is a valuable tool for probing many-body localization, phase transitions, and the dynamics of quantum information.

The key findings establish SRE as a powerful tool for characterizing quantum states and dynamics, going beyond traditional entanglement entropy. It highlights how SRE can reveal hidden order and correlations that are masked by total entanglement. The authors show how SRE evolves after a quantum quench, providing insights into relaxation and thermalization processes in different systems. They demonstrate that SRE can distinguish between different types of quenches and identify the relevant conserved quantities. A significant contribution is the use of SRE to probe the emergence of many-body localization in disordered systems.

The authors find that SRE exhibits characteristic features in the localized phase, such as a plateau in entanglement growth and a fragmentation of the quantum state. This provides a new way to diagnose and understand localization. The paper provides detailed analysis of SRE in free fermionic chains, which serve as a benchmark for more complex systems. The authors derive analytical results for certain cases and compare them with numerical simulations. The research is comprehensive, employing state-of-the-art numerical techniques and carefully validating the results.

Entanglement Channel Wave Governs Many-Body Dynamics

Researchers have identified a universal structure, termed the entanglement channel wave (ECW), governing the dynamics of many-body systems undergoing symmetry-resolved analysis. This ECW emerges consistently across diverse systems, U(1) fermions, U(1) bosons, and SU(2) spinful fermions, and persists regardless of the presence of interactions or disorder, establishing its fundamental nature. The team demonstrated this universality through systematic investigation across various regimes, utilizing both Krylov-subspace iterative methods and correlation matrix approaches. The ECW formalism allows for analytical determination of the correlation matrix spectrum in free fermions, providing a powerful tool for understanding entanglement properties.

Subsequent analysis reveals that the melting of the ECW exhibits signatures dependent on both symmetry and particle statistics, uncovering finer details in the growth of symmetry-resolved entanglement. This detailed structure provides insights into how entanglement evolves within these complex systems, moving beyond simple descriptions of overall entanglement growth. Further investigation into free fermions reveals a direct link between the ECW and the spectral properties of the correlation matrix. By leveraging the non-interacting nature of these systems, researchers showed that entanglement quantities can be efficiently computed by diagonalizing the correlation matrix.

The team derived a relationship between the correlation matrix spectrum and single-particle entanglement, providing a pathway to understand entanglement from measurable quantities. Specifically, the analysis demonstrates that the leading behavior of the correlation matrix eigenvalues for small times takes a predictable form, dependent on the shortest hopping distance between particles. This distance is classified by the parity of a symmetry quantum number, revealing a fundamental connection between symmetry and entanglement dynamics.

Entanglement Channel Wave Emerges as Universal Feature

This research identifies a universal pattern in the way entanglement evolves following a disturbance in many-body quantum systems, termed the entanglement channel wave (ECW). By examining systems of fermions and bosons, with and without interactions or disorder, the team demonstrates that this ECW consistently emerges as a short-time structure in symmetry-resolved entanglement dynamics. This suggests the ECW is a fundamental feature of quantum evolution, independent of particle type, interaction strength, or the presence of disorder. The investigation employed a Krylov-subspace iterative method to track the evolution of entanglement following a ‘quantum quench’, a sudden change to the system’s initial state. The results reveal that the ECW governs the initial stages of entanglement growth, providing a consistent framework for understanding complex quantum dynamics.