[论文解读] Non-equilibrium dynamics of the disordered Power of Two model

Kunal Singh, Sayan Choudhury|arXiv (Cornell University)|Mar 4, 2026

Quantum many-body systems被引用 0

一句话总结

论文研究现场无序如何影响稀疏二次方（PWR2）自旋模型的淬火动力学、混乱与谱性质，发现在有限大小下存在无序诱导的局域化，但在热力学极限下并无真正的多体局域化。

ABSTRACT

Motivated by recent experimental realizations of programmable spin models with long-range interactions, we investigate the non-equilibrium dynamics of the Power-of-Two (PWR2) model. This model consists of sparse long-range couplings between spin-$1/2$ objects separated by $d = 2^n$. In the absence of disorder, the system exhibits rapid scrambling and fast thermalization. We explore the impact of disorder in this system by analyzing the time evolution of the survival probability, half-chain entanglement entropy, and out-of-time-ordered correlators (OTOCs). We find that sufficiently strong disorder suppresses information spreading and induces localization. Remarkably, in the strong-disorder regime, the OTOCs display a non-monotonic spatial profile arising from the intrinsic nonlocality of the interactions, signaling qualitatively distinct scrambling dynamics compared to conventional long-range interacting systems. To characterize the localization transition, we extract the critical disorder strength $h_c$ from the spectral statistics and the eigenstate entanglement. We observe that $h_c$ increases with system size. Furthermore, at a fixed disorder strength, the eigenstate-averaged entanglement entropy increases with system size, while the inverse participation ratio decreases, indicating enhanced delocalization at larger sizes. These results collectively suggest that the PWR2 model remains ergodic in the thermodynamic limit for any finite disorder strength.

研究动机与目标

• 对可编程的稀疏长程自旋模型（PWR2）在现场无序下进行动机与分析。
• 通过淬火实验、存活概率、纠缠和OTOC来表征非平衡动力学。
• 研究谱统计与特征态属性以评估混沌与局域化。
• 确定无序是否在PWR2模型中驱动多体局域化转变。

提出的方法

• 用具有2的幂次范围的耦合和在[-h,h]中的随机场h_i来定义PWR2哈密顿量。
• 在来自特定初始态的淬火后，计算单自旋激发子系与零磁化子系的动力学。
• 评估时序无关相关函数C_ij(t)及空间平均的扰动散度（scrambling）。
• 在无序下分析存活概率和半链纠缠S(t)。
• 通过相邻隙比r等谱统计和特征态属性如纠缠熵、逆参与比P来研究谱统计。
• 评估系统大小依赖性以推断热力学极限行为。

Figure 1: (a) Schematic illustration of the Power of Two model with open boundary conditions. The interaction graph couples spins on sites separated by a power of two (see Eqns. 1 and 2 ). (b) The dynamics of the PWR2 model in the disorder-free limit ( $h=0$ ). The left panel shows the time-evolutio

实验结果

研究问题

• RQ1 无序是否在PWR2模型中诱导局域化，以及它如何影响信息扩散和混乱过程？
• RQ2 在PWR2模型中无序驱动的OTOC和纠缠增长表现为何，是否有多体局域化的证据？
• RQ3 随着无序和系统大小的变化，谱统计与特征态属性如何演化，对热力学极限下的遍历性有何含义？
• RQ4 在PWR2中是否存在有限尺寸的混沌到MBL转变，以及其临界无序强度是否随系统大小收敛或发散？

主要发现

• 无序抑制信息扩散和纠缠增长，在强h时偏向局域化样行为。
• 在强无序且存在非局部耦合时，OTOC呈现非单调的空间轮廓。
• 空间平均的OTOC在强无序区域趋于约0，表明散乱加剧的混乱速度下降。
• 存活概率在弱无序下迅速衰减，但在强无序下趋于更高的稳定值，表明记忆保留。
• 谱统计随着h增大从Wigner-Dyson向Poisson转移，但跨点随系统尺寸增大而移动，暗示在热力学极限下临界点h_c发散。
• 特征态纠缠随无序减小，而逆参与比在有限系统中指示局域化增强，但不足以在热力学极限下宣称MBL。
• 总体来说，对于任何有限无序强度，PWR2模型在热力学极限下仍然具有遍历性；随着系统规模增大，混沌行为仍然存在。

Figure 2: The time-evolution of the 1-magnon initial state, $|\psi\rangle_{\rm SM}$ (Eq. 3 ) for N=256 for various values of the disorder strength, $h$ . While, increasing disorder strength leads to greater localization, the spread of the magnon excitation does not follow a light-cone. Instead at st