Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
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DOI：
10.1103/physrevb.99.134305
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发表时间：
2019-04-16
影响因子：
3.7
通讯作者：
Huse, David A.
中科院分区：
文献类型：
--
作者：
Gopalakrishnan, Sarang;Huse, David A.
多体局域化（MBL）相变不是传统的热力学相变。因此，为了定义相变，人们应该允许以一种不同于传统热力学极限的方式来取无限系统的极限。我们探讨了所谓的雪崩不稳定性，由于罕见的热化区域在MBL阶段的淬火随机性的系统在两种情况下：在一个以上的空间维度的短程相互作用系统和系统中的相互作用脱落的距离作为一个幂律。我们找到了一种非传统的方法来缩放这些系统，使它们确实有一种相变。我们的论证表明，在一维以上的短程相互作用（或具有足够快的衰减幂律）的系统中，MBL相变是本征态纠缠开始扩散到一些典型区域的过渡：过渡是由雪崩开始时设定的。一旦这种纠缠开始，系统就会热化。从这个角度来看，研究较多的情况下，一维MBL与短程相互作用是一个特殊的情况下，不同的，在某些方面更传统的，相变类型。
The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus, to define the phase transition, one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called avalanche instability due to rare thermalizing regions in the MBL phase for systems with quenched randomness in two cases: for short-range interacting systems in more than one spatial dimension and for systems in which the interactions fall off with distance as a power law. We find an unconventional way of scaling these systems so that they do have a type of phase transition. Our arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension (or with sufficiently rapidly decaying power laws) is a transition where entanglement in the eigenstates begins to spread into some typical regions: The transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.