多体局域化：稳定性与不稳定性。
Many-body localization: stability and instability.
作者信息
De Roeck Wojciech, Imbrie John Z
机构信息
Instituut voor Theoretische Fysica, KU Leuven, 3000 Leuven, Belgium.
Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA
出版信息
Philos Trans A Math Phys Eng Sci. 2017 Dec 13;375(2108). doi: 10.1098/rsta.2016.0422.
Rare regions with weak disorder (Griffiths regions) have the potential to spoil localization. We describe a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension, under a physically reasonable assumption on the statistics of eigenvalues. We discuss ideas about the situation in higher dimensions, where one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions. We argue that ergodicity is restored in dimension >1, although equilibration should be extremely slow, similar to the dynamics of glasses.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
具有弱无序性的稀有区域（格里菲斯区域）有可能破坏局域化。在关于本征值统计的一个物理上合理的假设下，我们描述了一维弱相互作用自旋链的局域运动积分（LIOMs）的非微扰构造。我们讨论了关于更高维度情形的一些想法，在更高维度中，人们不再能确保涉及格里菲斯区域的相互作用远小于此类区域的典型能级间距。我们认为在维度大于1时遍历性得以恢复，尽管平衡应该极其缓慢，类似于玻璃的动力学。本文是主题为“量子系统中遍历性的崩溃：从固体到合成物质”这一特刊的一部分。
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