标题： 量子随机能量模型中迁移率边的标度分析和重整化群 显示英文标题

标题： Scaling Analysis and Renormalization Group on the Mobility Edge in the Quantum Random Energy Model

摘要： 在通过重整化群（RG）研究安德森和多体局域化的最新进展基础上，我们考察了量子随机能量模型（QREM）中的局域化标度理论。 QREM 在有限能量密度下会发生局域化-非局域化相变，而在能谱中心仍保持完全遍历性。 在零能量密度下，我们表明 RG 轨迹一致流向遍历相，并且在遍历固定点附近表现出非传统的分形维度标度。 当按前向散射近似方法建议的方式对无序幅度进行重标度时，在能谱中心也会出现局域化相变，其特性类似于扩展图上的安德森相变。 在有限能量密度下，无需对无序进行重标度就会发生局域化相变，但其表现出与扩展图上观察到的标度行为类似。 在无序重标度下，该模型的普适类保持不变，反映了 RG 对微观细节的独立性。 我们的发现展示了随机图标度行为的鲁棒性，并为多体局域化相变提供了新的见解。 显示英文摘要

摘要： Building on recent progress in the study of Anderson and many-body localization via the renormalization group (RG), we examine the scaling theory of localization in the quantum Random Energy Model (QREM). The QREM is known to undergo a localization-delocalization transition at finite energy density, while remaining fully ergodic at the center of the spectrum. At zero energy density, we show that RG trajectories consistently flow toward the ergodic phase, and are characterized by an unconventional scaling of the fractal dimension near the ergodic fixed point. When the disorder amplitude is rescaled, as suggested by the forward scattering approximation approach, a localization transition emerges also at the center of the spectrum, with properties analogous to the Anderson transition on expander graphs. At finite energy density, a localization transition takes place without disorder rescaling, and yet it exhibits a scaling behavior analogous to the one observed on expander graphs. The universality class of the model remains unchanged under the rescaling of the disorder, reflecting the independence of the RG from microscopic details. Our findings demonstrate the robustness of the scaling behavior of random graphs and offer new insights into the many-body localization transition.