Subdiffusion in a disordered spin chain with random dephasing: Finite-size corrections, Griffiths effects, and implications for many-body localization
Subdiffusion in a disordered spin chain with random dephasing: Finite-size corrections, Griffiths effects, and implications for many-body localization
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具有随机相移的无序自旋链中的次扩散：有限尺寸校正、格里菲斯效应以及对多体定位的影响
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发表时间：
2020
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通讯作者：
A. Scardicchio
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作者：
S. Taylor;A. Scardicchio
我们研究了具有现场无序和随机定位的现场失相的边界驱动 XX 自旋链中的传输，观察到低于失相位点的临界密度从扩散到亚扩散自旋传输的转变。然后，我们提出了一个完全可解的导体和绝缘体半经典模型，该模型表现出扩散相和次扩散相，并定性地再现了量子系统的结果。这些模型中的次扩散是稀有绝缘区域的结果，因此它们在更受控的设置中表现出“格里菲斯效应”物理现象，据推测，这种效应会导致在相互作用的多体可定位系统中观察到的次扩散传输。对于量子模型，我们表明有限尺寸效应来自三种特征长度的相互作用：一种与无序（局域化长度）相关，一种与相移相关，第三种与定义大的、稀有的绝缘区域的渗滤问题相关。后者随着系统规模呈对数增长，我们推测这可能是为什么在次扩散相互作用系统中没有观察到典型的格里菲斯效应的重尾分布的原因。
We study transport in the boundary-driven XX spin chain with onsite disorder and randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a critical density of sites with dephasing. We then present an exactly solvable semiclassical model of conductors and insulators, which exhibits both diffusive and subdiffusive phases, and qualitatively reproduces the results of the quantum system. The subdiffusion in these models is a consequence of rare insulating regions, and they therefore exhibit, in a more controlled setup, the physics of "Griffiths effects" which have been conjectured to cause the subdiffusive transport observed in interacting many-body localizable systems. For the quantum model we show that finite-size effects come from the interplay of three characteristic lengths: one associated with disorder (the localization length), one with dephasing, and the third with the percolation problem defining large, rare, insulating regions. The latter grows logarithmically with system size, and we conjecture that this may be the reason why the heavy-tailed distributions typical of Griffiths effects have not been observed in subdiffusive interacting systems.