Genuine Multipartite Entanglement Signals Ergodic-to-Many-Body Localized Transition in Spin Chains

Understanding how disorder affects complex quantum systems remains a central challenge in condensed matter physics, and recent work by Triyas Sapui, Keshav Das Agarwal, and Tanoy Kanti Konar, along with colleagues at the Harish-Chandra Research Institute and the University of Trento, sheds new light on this problem. The researchers demonstrate that genuine multipartite entanglement, a strong form of quantum correlation, can reliably signal the transition between a state of quantum chaos and a state known as many-body localization. Their investigation of disordered spin chains, incorporating interactions known as Dzyaloshinskii-Moriya interactions, reveals that entanglement vanishes when the system becomes localized, providing a novel way to identify this critical point. Importantly, the team finds that specific interactions actually stabilise the chaotic phase, delaying the onset of localization, and this effect is consistently reflected in the entanglement measurements, establishing it as a robust diagnostic tool for understanding these complex quantum phenomena.

The core theme is MBL, with numerous studies exploring its theoretical foundations, numerical simulations, and experimental observations. A significant portion of the research focuses on the behaviour of quantum systems with disorder, and the contrast between MBL, which prevents energy flow, and systems that readily thermalize. The Dzyaloshinskii-Moriya interaction (DMI) frequently appears as a means of introducing disorder or creating unique quantum effects.

Many references also address quantifying entanglement, characterizing quantum states, and using entanglement to diagnose MBL. A large number of studies detail the computational techniques used to investigate these systems, including methods like Lanczos, kernel polynomial methods, and exact diagonalization. Finally, some references point to experimental work observing signatures of MBL or related phenomena. The research can be categorized to improve understanding. Theoretical studies lay the foundations of MBL and disordered systems, while others focus on the DMI and its application in magnetic materials.

A third category explores entanglement and its role in characterizing MBL, and a fourth details the numerical methods used in these simulations. Further categories cover quantum chaos and thermalization, and experimental observations of MBL. This bibliography is a valuable resource for anyone working in this field, offering a comprehensive overview of the current state of research.

Entanglement Reveals Ergodic and Localized Quantum Phases

Researchers have discovered a reliable method for identifying the transition between two distinct states of matter: an ergodic phase where energy flows freely, and a many-body localized (MBL) phase where energy remains trapped. This transition is crucial for understanding disordered quantum systems, and the new method focuses on measuring the degree of multipartite entanglement within the system. The research demonstrates that high levels of entanglement consistently appear in the ergodic phase, while entanglement vanishes completely as the system enters the MBL phase. The team established this connection by calculating a quantity representing genuine multipartite entanglement, revealing a clear correlation between its value and the system’s phase.

Specifically, the entanglement measure saturates at a finite value in the ergodic phase, but steadily decreases and ultimately disappears when the system becomes localized. This provides a robust indicator of the transition point, aligning with other established methods. The findings suggest that the MBL phase is unsuitable for quantum technologies that rely on maintaining strong entanglement between multiple particles. Interestingly, the inclusion of specific interactions, known as Dzyaloshinskii-Moriya (DM) interactions, significantly alters the system’s behaviour. These interactions, arising from spin-orbit coupling, introduce long-range correlations between spins and broaden the range of conditions under which the ergodic phase persists. The research shows that increasing the strength of DM interactions delays the onset of localization, requiring a stronger degree of disorder to drive the system into the MBL phase. Notably, three-body DM interactions are particularly effective at stabilizing the ergodic phase compared to two-body interactions, suggesting that manipulating these interactions could offer a pathway to engineer materials with enhanced stability and control over energy flow.

Entanglement Detects Ergodic to Localized Transition

This research demonstrates that genuine multipartite entanglement can reliably indicate the transition between ergodic and many-body localized (MBL) phases in disordered quantum spin chains. By employing a computable measure of entanglement, the team found that its value in the middle of the energy spectrum accurately identifies the critical disorder strength at which this transition occurs, aligning with established indicators like the gap ratio and correlation length. The study reveals that the inclusion of Dzyaloshinskii-Moriya interactions stabilizes the ergodic phase, delaying the onset of localization and shifting the transition point to higher disorder strengths. Furthermore, the dynamics of multipartite entanglement, starting from a simple initial state, also reveals the transition, with the growth rate of entanglement decreasing as the system enters the localized phase.

The team observed that the steady-state entanglement scales differently depending on the phase, exhibiting sub-area-law behaviour in the localized phase and sub-volume-law scaling in the ergodic phase. The authors acknowledge that their analysis focuses on specific system parameters and initial states, and future work could explore the behaviour across a wider range of conditions and investigate the impact of stronger interactions. This accessible measure of entanglement offers a promising tool for characterizing MBL transitions and could be implemented in current quantum simulators to further explore these complex quantum phenomena.