We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity $\sigma \left(\omega \right)$ and the return probability $R\left(\tau \right)$ and study their average low-frequency and long-time power-law behavior, respectively. We show that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and find that the diffusive and MBL regimes of the quasiperiodic model are more robust than those in the random system. Using the distribution of the dc conductivity, we quantify the contribution of sample-to-sample and state-to-state fluctuations of $\sigma \left(\omega \right)$ across the MBL transition. We find that the activated dynamical scaling ansatz works poorly in the quasiperiodic model but holds in the random model with an estimated activation exponent $\psi \approx 0.9$. We argue that near the MBL transition in quasiperiodic systems, critical eigenstates give rise to a subdiffusive crossover regime on finite-size systems.

中文翻译：

---

跨周期和随机系统中跨多体本地化过渡的传输特性

我们从理论上研究了在无限温度下一维相互作用拟周期系统中的输运性质。我们比较并对比了在准周期模型和随机模型中跨多体定位（MBL）过渡的动力学传输属性。使用精确的对角化，我们可以计算出光导$\sigma （\omega ）$ 和返回概率 $\mathrm{[R}（\tau ）$并分别研究它们的平均低频和长时间幂律行为。我们表明，低能输运动力学在准周期和随机模型的热相和MBL阶段均显着不同，并且发现准周期模型的扩散和MBL机制比随机系统的鲁棒性更高。利用直流电导率的分布，我们可以量化样品之间的样品变化和状态之间的波动。$\sigma （\omega ）$跨MBL过渡。我们发现，激活的动态缩放ansatz在拟周期模型中效果不佳，但在具有估计的激活指数的随机模型中保持有效$\psi \approx 0.9$。我们认为，在准周期系统的MBL跃迁附近，临界本征态在有限尺寸系统上引起了亚扩散交叉机制。