Quantum Avalanche Stability Achieves Critical Interaction Exponent of 1

Researchers are increasingly focused on understanding the stability of many-body localisation (MBL), a fascinating phase of matter resisting thermalisation! Longhui Shen, Bin Guo, and Zhaoyu Sun, from Wuhan University of Technology and Wuhan Polytechnic University, alongside their colleagues, have now investigated avalanche instabilities within this MBL phase in one-dimensional systems with long-range interactions! Their work, utilising both exact diagonalisation and Lindblad master equation simulations, reveals a critical interaction exponent separating fragile and robust regimes of MBL, and crucially, establishes a quantitative stability criterion for maintaining localisation! This discovery resolves ongoing theoretical debates surrounding long-range MBL and offers a clear pathway towards observing these quantum phenomena in emerging experimental platforms like Rydberg atom arrays , potentially paving the way for more robust quantum technologies.

Long-range MBL phase stability in spin chains remains

Scientists have demonstrated the asymptotic stability of the many-body localized (MBL) phase in one-dimensional Heisenberg spin chains featuring long-range power-law interactions! The team achieved this breakthrough by combining exact diagonalization with Lindblad master equation simulations, systematically mapping the interplay between interaction range and disorder strength. This research unveils a critical interaction exponent of approximately 2, separating a fragile regime, where critical disorder diverges exponentially, from a robust short-range regime. To rigorously test resistance to thermalization, researchers coupled the boundary of the system to an infinite-temperature bath and meticulously tracked the propagation of the thermalization front into the localized bulk, providing a novel method for assessing MBL stability.
The study establishes a unified scaling law for the characteristic thermalization time, expressed as Trth ∼exp[κ(α)LW], where L represents the system size and W denotes the disorder intensity! This exponential divergence with the product of size and disorder strength confirms a significant suppression of thermalization, enabling the derivation of a quantitative stability criterion, Wstab(α), which defines the minimum critical disorder strength needed to maintain avalanche stability. Finite-size scaling analysis of entanglement entropy was performed to identify the critical interaction exponent, providing a precise delineation between regimes of differing stability. By probing the dynamics of the thermalization front, the team quantified the expansion of the thermalized region, observing a slow logarithmic growth consistent with predictions for localized systems.

Experiments show that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold, resolving ongoing theoretical debates surrounding long-range MBL! This work bridges a critical gap in understanding the behaviour of these complex quantum systems, offering a roadmap for observing these dynamics in experimental platforms such as Rydberg atom arrays. The research establishes a clear phase diagram of Wstab(α), revealing that short-range interactions enhance robustness while long-range connectivity promotes fragility, providing valuable insights for the design and control of MBL systems. This innovative approach combines static and dynamic methods, offering a comprehensive understanding of the interplay between interaction range and disorder strength in MBL systems.

Long-Range Interactions and MBL Phase Stability are crucial

Scientists investigated the stability of the many-body localized (MBL) phase against avalanche instabilities within a one-dimensional Heisenberg spin chain featuring long-range power-law interactions, defined as V ∝ r−α ! The research team combined exact diagonalization, used to determine static properties, with Lindblad master equation simulations of open-system dynamics to systematically map the interplay between interaction range and disorder strength ! This hybrid approach enabled a comprehensive analysis of the system’s behaviour under varying conditions. To rigorously characterise the system, the study pioneered a finite-size scaling analysis of entanglement entropy, identifying a critical interaction exponent αc ≈ 2.

This exponent delineates a fragile regime, where the critical disorder diverges exponentially, from a more robust short-range regime, revealing the conditions under which the MBL phase becomes susceptible to instability. Researchers then engineered a controlled open-system setup. This dynamical suppression enabled derivation of a quantitative stability criterion, Wstab(α), representing the minimum critical disorder strength required for asymptotic avalanche stability ! The resulting phase diagram, Wstab(α), highlights that short-range interactions enhance robustness, while long-range connectivity promotes fragility, offering insights into MBL behaviour in experimental platforms such as Rydberg atom arrays and advancing understanding of quantum many-body systems ! The work confirms that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold.

Long-range interactions stabilise spin chain localisation, preventing thermalisation

Scientists investigated the stability of the localized phase against avalanche instabilities in a one-dimensional Heisenberg spin chain featuring long-range power-law interactions! Through a combination of exact diagonalization and Lindblad master equation simulations, the team systematically mapped the interplay between interaction range and disorder strength. Finite-size scaling analysis of entanglement entropy identified a critical interaction exponent of approximately 2, separating a fragile regime, characterized by exponentially diverging critical disorder, from a robust short-range regime! Experiments revealed that the characteristic thermalization time follows a unified scaling law, Trth ∼exp[κ(α)LW], where L represents the system size and W denotes the disorder intensity.

This scaling demonstrates an exponential divergence with the product of system size and disorder strength, effectively suppressing thermalization in the localized bulk. Measurements confirm that this suppression enables the derivation of a quantitative stability criterion, Wstab(α), representing the minimum critical disorder strength required to maintain avalanche stability! The research conclusively shows that the Many-Body Localized (MBL) phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold. Data shows that deep within the MBL phase, thermalization progresses with a slow logarithmic growth over time, consistent with the prediction of a “logarithmic light cone” in localized systems.

By probing the dynamics of the thermalization front, scientists quantified the expansion of the thermalized region and established a lower bound on thermalization timescales. The team coupled the boundary of the system to an infinite-temperature bath, tracking the propagation of the thermalization front into the localized bulk to rigorously test resistance to avalanches. Results demonstrate the derivation of a phase diagram of Wstab(α), highlighting that short-range interactions enhance robustness while long-range connectivity promotes fragility! This work bridges theoretical debates on long-range MBL and provides a roadmap for observing these dynamics in experimental platforms such as Rydberg atom arrays. The breakthrough delivers a quantitative understanding of MBL stability, offering insights into quantum information technology and condensed matter theory.

Long-Range MBL Stability and Critical Exponent are key

Scientists have demonstrated the asymptotic stability of the Many-Body Localisation (MBL) phase in one-dimensional Heisenberg spin chains featuring long-range power-law interactions! Through a combination of exact diagonalization and Lindblad master equation simulations, researchers systematically investigated the interplay between interaction range and disorder strength, revealing a critical interaction exponent of approximately 2. This exponent delineates a fragile regime, where critical disorder diverges exponentially, from a more robust short-range regime. Furthermore, the study established a quantitative stability criterion, defining the minimum disorder strength needed to prevent avalanche instabilities.

Finite-size scaling analysis of entanglement entropy and tracking the propagation of thermalization fronts confirmed that the characteristic thermalization time scales exponentially with both system size and disorder intensity. These findings bridge ongoing theoretical debates concerning long-range MBL, offering a pathway for experimental observation using platforms like Rydberg atom arrays. The authors acknowledge that their reported errors reflect only numerical fitting precision and do not fully capture the uncertainty inherent in scaling behaviour near divergence points. They also note that the power-law description breaks down for strong long-range interactions, and finite-size effects may influence the precise determination of critical exponents. Future research employing tensor network algorithms could access larger system sizes and definitively verify the Harris bound, further solidifying these results and enhancing our understanding of MBL transitions.