发表机构
University of Tokyo; RIKEN Pioneering Research Institute (PRI); University of Warwick; RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS); RIKEN; Ritsumeikan University（东京大学; 理化学研究所先锋研究本部; 华威大学; 理化学研究所交叉理论与数学科学中心; 理化学研究所; 立命馆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究受监测一维马约拉纳链的有效哈密顿量，发现长程幂次跳跃的关联使纠缠熵呈[ln(L)]²标度，揭示该关联是非常规纠缠标度的成因。
AI 中文摘要
我们通过李雅普诺夫谱分析研究描述一维马约拉纳链受监测动力学的有效哈密顿量结构，重点关注其无隙相特征：有限尺寸标度与常规临界系统、无 frustration（无挫败）系统不同，谱隙闭合速度快于1/L但慢于1/L²，纠缠熵随系统尺寸L呈[ln(L)]²增长。我们发现对应的有效哈密顿量具有随机长程幂次跳跃，且跳跃幅度存在非平凡关联，并非独立同分布。为阐明这些非高斯关联的作用，我们构建了随机幂次跳跃模型以捕捉有效哈密顿量的核心特征，该模型的谱隙衰减速度同样快于1/L但慢于1/L²。进一步研究发现，当跳跃无关联时，基态纠缠呈ln(L)标度；而存在关联时，纠缠熵被增强，在研究的系统尺寸范围内，其与系统尺寸的依赖关系符合[ln(L)]²标度。这些结果表明，长程跳跃幅度间的关联是导致常规孤立量子系统基态中极少出现的纠缠标度的原因。
英文摘要
We investigate the structures of effective Hamiltonians governing monitored dynamics of a one-dimensional Majorana chain through the Lyapunov spectral analysis. We focus on a gapless phase characterized by finite-size scalings different from those in conventional critical and/or frustration-free systems; the spectral gap closing faster than $1/L$ but slower than $1/L^2$ and the entanglement entropy growing as $[\ln(L)]^2$ with $L$ being the system size. We find that the corresponding effective Hamiltonians have random long-range power-law hoppings with nontrivial magnitude correlations, rather than being independently and identically distributed. To elucidate the role of these non-Gaussian correlations, we construct random power-law hopping models that capture the essential features of the effective Hamiltonians. The spectral gaps of the constructed models decay faster than $1/L$ but slower than $1/L^2$. We find that, in the absence of hopping correlations, the ground-state entanglement exhibits $\ln(L)$ scaling. In the presence of correlations, by contrast, the entanglement entropy is enhanced and its system-size dependence is consistent with $[\ln(L)]^2$ scaling over the system sizes studied. These results suggest that correlations among long-range hopping magnitudes are responsible for the entanglement scaling that seldom appears in ground states of conventional isolated quantum systems.
Comments12 pages, 9 figures
