We analyze the finite-size scaling of the average gap ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin chain with quasiperiodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of the Berezinskii-Kosterlitz-Thouless transition, the same as in the case of uniformly disordered systems as advocated in recent studies. Moreover, we observe that the critical disorder strength shows a clear sublinear drift with the system size as compared to the linear drift seen in random disordered models, suggesting that the finite-size effects in the MBL transition for the QP systems are less severe than that in the random disordered scenario. Moreover, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of on-site magnetizations that can be traced back to the strong correlations present in the QP potential.

中文翻译：

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准周期自旋链中多体局域化跃迁的有限尺度分析

我们分析了具有准周期 (QP) 势的一维海森堡自旋链中多体定位 (MBL) 跃迁的平均间隙比和纠缠熵的有限尺寸缩放。通过使用最近引入的成本函数方法，我们使用多达 22 个格点的系统的精确对角化来比较不同的转换场景。我们的研究结果表明，QP 海森堡链中的 MBL 转变属于 Berezinskii-Kosterlitz-Thouless 转变的类别，与最近研究中提倡的均匀无序系统的情况相同。此外，我们观察到，与随机无序模型中看到的线性漂移相比，临界无序强度显示出明显的随系统大小的次线性漂移，这表明 QP 系统的 MBL 过渡中的有限尺寸效应不如随机无序情况下的严重。此外，在遍历机制的深处，我们发现了现场磁化分布的意外双峰结构，这可以追溯到 QP 电位中存在的强相关性。