标题： 自旋和能量扩散与亚扩散在无序自旋链中 显示英文标题

标题： Spin and energy diffusion vs. subdiffusion in disordered spin chains

摘要： 虽然在具有随机局部场的自旋链中高温自旋扩散已经被许多研究涉及，这些研究关注的是多体局域化（MBL）现象，但相同模型中的能量扩散却很少被探索。 我们证明，在弱随机场下能量扩散更快，但在强场下变得基本相等；因此，这两种扩散决定了系统中最慢的弛豫时间尺度（Thouless时间）。 数值上可达到的有限尺寸系统显示了相对于实际场配置的扩散常数异常大的分布。 尽管扩散对场强度呈指数-like依赖，但结果对于扭曲边界条件的敏感性与局域化的Thouless准则以及假设的向MBL的转变不兼容，至少对于数值上可达到的尺寸而言是如此。 相反，我们在动力学扩散响应中发现了亚扩散传输场景的迹象。 显示英文摘要

摘要： While the high-temperature spin diffusion in spin chains with random local fields has been the subject of numerous studies concerning the phenomenon of many-body localization (MBL), the energy diffusion in the same models has been much less explored. We demonstrate that energy diffusion is faster at weak random fields but becomes essentially equal at strong fields; hence, both diffusions determine the slowest relaxation time scale (Thouless time) in the system. Numerically reachable finite-size systems reveal the anomalously large distribution of diffusion constants with respect to actual field configurations. Despite the exponential-like dependence of diffusion on field strength, the results for sensitivity to twisted boundary conditions are incompatible with the Thouless criterion for localization and the presumed transition to MBL, at least for numerically reachable sizes. In contrast, we find indications of the scenario of subdiffusive transport, particularly in the dynamical diffusivity response.