Quantum Avalanche Stability of Many-Body Localization with Power-Law Interactions
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| Format: | Preprint |
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2026
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| author | Shen, Longhui Guo, Bin Sun, Zhaoyu |
| author_facet | Shen, Longhui Guo, Bin Sun, Zhaoyu |
| contents | We investigate the stability of the many-body localized phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions ($V\propto r^{-α}$). By combining exact diagonalization of static properties with Lindblad master equation simulations of open-system dynamics, we systematically map the interplay between interaction range and disorder strength. Our finite-size scaling analysis of entanglement entropy identifies a critical interaction exponent $α_c \approx 2$, which separates a fragile regime, characterized by an exponentially diverging critical disorder, from a robust short-range regime. To rigorously test the system's resistance to avalanches, we couple the boundary to an infinite-temperature bath and track the propagation of the thermalization front into the localized bulk. We find that the characteristic thermalization time follows a unified scaling law, $T_{r_{\text{th}}} \sim \exp[κ(α) LW]$ (herein, $L$ is the system size, and $W$ is the disorder intensity), which diverges exponentially with the product of system size and disorder strength. This suppression enables the derivation of a quantitative stability criterion, $W_{\text{stab}}(α)$, representing the minimum critical disorder strength required to maintain avalanche stability. Our results confirm that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold, bridging theoretical debates on long-range MBL and providing a roadmap for observing these dynamics in experimental platforms such as Rydberg atom arrays. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13485 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Avalanche Stability of Many-Body Localization with Power-Law Interactions Shen, Longhui Guo, Bin Sun, Zhaoyu Disordered Systems and Neural Networks Statistical Mechanics We investigate the stability of the many-body localized phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions ($V\propto r^{-α}$). By combining exact diagonalization of static properties with Lindblad master equation simulations of open-system dynamics, we systematically map the interplay between interaction range and disorder strength. Our finite-size scaling analysis of entanglement entropy identifies a critical interaction exponent $α_c \approx 2$, which separates a fragile regime, characterized by an exponentially diverging critical disorder, from a robust short-range regime. To rigorously test the system's resistance to avalanches, we couple the boundary to an infinite-temperature bath and track the propagation of the thermalization front into the localized bulk. We find that the characteristic thermalization time follows a unified scaling law, $T_{r_{\text{th}}} \sim \exp[κ(α) LW]$ (herein, $L$ is the system size, and $W$ is the disorder intensity), which diverges exponentially with the product of system size and disorder strength. This suppression enables the derivation of a quantitative stability criterion, $W_{\text{stab}}(α)$, representing the minimum critical disorder strength required to maintain avalanche stability. Our results confirm that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold, bridging theoretical debates on long-range MBL and providing a roadmap for observing these dynamics in experimental platforms such as Rydberg atom arrays. |
| title | Quantum Avalanche Stability of Many-Body Localization with Power-Law Interactions |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2601.13485 |