多体局域化交叉中Fock空间异质性的统计层次与空间模式
Statistical levels and spatial modes of Fock-space heterogeneity in many-body localization crossovers
浏览论文内容
中文总结 AI 辅助
本研究提出基于构型空间距离分布的方差分解框架，解析多体局域化交叉中异质性的统计层次与空间模式，揭示随机与准周期系综的差异及样本间波动机制。
中文摘要 AI 辅助
在多体局域化交叉附近，局部记忆在本征态和系综实现之间强烈波动，但观察到的异质性结合了不同统计层次的贡献。我们开发了一个基于构型空间距离分布的统计框架，利用方差分解来分离本征态内部、单个样本的本征态之间以及样本之间的波动。将该框架应用于具有相同单点场边缘的随机余弦和准周期余弦Ising系综，我们发现，在所研究的精确对角化尺寸下，最明显的差异出现在无序实现或准周期相位样本之间，而本征态内部和样本内本征态间的贡献大致相当。空间协方差表明，随机外部波动具有更强的均匀分量，而准周期相位波动在有限波数上组织得更强，并在控制距离中心的空间平均中部分抵消。我们发现，在随机系综的交叉附近，系综平均的距离中心对名义场强的变化特别敏感。结合实现场振幅的样本间差异，这种平均响应解释了距离中心的大部分样本间变化。对半链纠缠的分析进一步表明，其样本间波动同样反映了振幅变化及其自身平均响应的综合效应。对固定磁化自旋链的应用展示了该框架在约束构型空间中的适用性。因此，解析统计层次和空间模式为样本依赖的多体记忆及其构型空间概率几何提供了更完整的图景。
英文摘要
Near many-body localization crossovers, local memory fluctuates strongly among eigenstates and ensemble realizations, but the observed heterogeneity combines contributions from different statistical levels. We develop a statistical framework based on configuration-space distance distributions that uses a variance decomposition to separate fluctuations within eigenstates, between eigenstates of one sample, and between samples. Applying this framework to random-cosine and quasiperiodic-cosine Ising ensembles with the same one-site field marginal, we find that, at the exact-diagonalization sizes studied, the clearest difference occurs among disorder realizations or quasiperiodic phase samples, whereas within-eigenstate and within-sample eigenstate-to- eigenstate contributions remain broadly comparable. Spatial covariances show that random outer fluctuations have a much stronger uniform component, whereas quasiperiodic phase fluctuations are organized more strongly at finite wave number and partly cancel in the spatial average controlling the distance center. We find that, near the crossover in the random ensemble, the ensemble-averaged distance center is particularly sensitive to changes in the nominal field strength. Combined with sample-to-sample differences in the realized field amplitude, this mean response accounts for much of the sample-to-sample variation in the distance center. Analysis of half-chain entanglement further shows that its sample-to-sample fluctuations likewise reflect the combined effects of amplitude variations and its own mean response. An application to a fixed-magnetization spin chain demonstrates the framework in a constrained configuration space. Resolving both statistical level and spatial mode therefore provides a more complete picture of sample- dependent many-body memory and its configuration-space probability geometry.
发表机构
- Lanzhou University（兰州大学）
机构由 AI 辅助整理，请以论文原文为准。
