Many-body localized (MBL) systems do not approach thermal equilibrium under their intrinsic dynamics; MBL and conventional thermalizing systems form distinct dynamical phases of matter, separated by a phase transition at which equilibrium statistical mechanics breaks down. True MBL is known to occur only under certain stringent conditions for perfectly isolated one-dimensional systems, with Hamiltonians that have strictly short-range interactions and lack any continuous non-Abelian symmetries. However, in practice, even systems that are not strictly MBL can be nearly MBL, with equilibration rates that are far slower than their other intrinsic timescales; thus, anomalously slow relaxation occurs in a much broader class of systems than strict MBL. In this review we address transport and dynamics in such nearly-MBL systems from a unified perspective. Our discussion covers various classes of such systems: (i) disordered and quasiperiodic systems on the thermal side of the MBL-thermal transition; (ii) systems that are strongly disordered, but obstructed from localizing because of symmetry, interaction range, or dimensionality; (iii) multiple-component systems, in which some components would in isolation be MBL but others are not; and finally (iv) driven systems whose dynamics lead to exponentially slow rates of heating to infinite temperature. A theme common to many of these problems is that they can be understood in terms of approximately localized degrees of freedom coupled to a heat bath (or baths) consisting of thermal degrees of freedom; however, this putative bath is itself nontrivial, being either small or very slowly relaxing. We discuss anomalous transport, diverging relaxation times, and other signatures of the proximity to MBL in these systems. We also survey recent theoretical and numerical methods that have been applied to study dynamics on either side of the MBL transition.

中文翻译：

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多体定位阈值处的动力学和传输

多体局域化 (MBL) 系统在其固有动力学下不会接近热平衡；MBL 和传统的热化系统形成不同的物质动态相，由相变分隔，在该相变处平衡统计力学分解。已知真正的 MBL 仅在完全孤立的一维系统的某些严格条件下发生，哈密顿量具有严格的短程相互作用并且缺乏任何连续的非阿贝尔对称性。然而，在实践中，即使不是严格 MBL 的系统也可能接近 MBL，其平衡速率远低于其他固有时间尺度；因此，异常缓慢的松弛发生在比严格 MBL 更广泛的系统类别中。在这篇综述中，我们从统一的角度讨论了这种近 MBL 系统中的传输和动力学问题。我们的讨论涵盖了各种类型的此类系统：（i）MBL-热转变热侧的无序和准周期系统；(ii) 严重无序但由于对称性、相互作用范围或维度而无法定位的系统；(iii) 多组件系统，其中一些组件单独是 MBL，但其他组件不是；最后（iv）驱动系统，其动力学导致加热到无限温度的速度呈指数级缓慢。许多这些问题的一个共同主题是，它们可以通过耦合到由热自由度组成的一个（或多个）热浴的近似局部自由度来理解；然而，这个假定的浴缸本身并不平凡，要么很小，要么非常缓慢地放松。我们讨论异常传输、发散弛豫时间、以及这些系统中与 MBL 接近的其他特征。我们还调查了最近用于研究 MBL 过渡两侧动力学的理论和数值方法。