Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is, however, nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit but are challenging for models without translational invariance. Here we demonstrate that NLCE provides a powerful tool to explore MBL by simulating quench dynamics in disordered spin-$1/2$ two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an efficient real-time evolution of pure states, we obtain converged results for the decay of the imbalance on long time scales and show that, especially for intermediate disorder below the putative MBL transition, NLCE outperforms direct simulations of finite systems with open or periodic boundaries. Furthermore, while spin is delocalized even in strongly disordered Hubbard chains with frozen charge, we unveil that an additional tilted potential leads to a drastic slowdown of the spin imbalance and nonergodic behavior on accessible times. Our work sheds light on MBL in systems beyond the well-studied disordered Heisenberg chain and emphasizes the usefulness of NLCE for this purpose.

中文翻译：

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热力学极限下的多体定位和离域动力学

经历多体定位（MBL）跃迁的无序量子系统在其自身动力学下无法达到热平衡。然而，由于有限尺寸效应，基于数值结果区分渐近局部化或非局部化动力学是不平凡的。数值链接簇扩展 (NLCE) 提供了一种在热力学极限下直接处理量子系统的方法，但对于没有平移不变性的模型来说具有挑战性。在这里，我们证明 NLCE 通过模拟无序自旋中的淬火动力学提供了探索 MBL 的强大工具。$1/2$两腿梯和费米-哈伯德链。将 NLCE 与纯状态的有效实时演化相结合，我们获得了长时间尺度上不平衡衰减的收敛结果，并表明，特别是对于假定的 MBL 过渡以下的中间无序，NLCE 优于具有开放式的有限系统的直接模拟或周期性边界。此外，虽然即使在具有冻结电荷的强无序哈伯德链中自旋也是离域的，但我们揭示了额外的倾斜电位会导致自旋不平衡和可访问时间的非遍历行为急剧减慢。我们的工作揭示了经过充分研究的无序海森堡链之外的系统中的 MBL，并强调了 NLCE 对此目的的有用性。