The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension $d>1$, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension $d>1$. We argue that (i) the MBL phase is stable against “avalanches” at strong enough quasiperiodic modulations for $d=2$, and (ii) the possibility of an avalanche strongly constrains the finite-size scaling behavior of the MBL transition. We present a suggestive construction that MBL is unstable for $d\ge 3$.

中文翻译：

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维度> 1的准周期多体定位跃迁

近年来，多体定位（MBL）跃迁的性质，甚至随机多体量子系统中MBL相的存在都引起了激烈的争论。在空间维度$d>1$，有一些共识是，MBL 相对稀有的热夹杂物不稳定，这可能导致整个系统热化的雪崩。在这篇笔记中，我们探讨了 MBL 在维度上的准周期系统中的可能性$d>1$. 我们认为 (i) MBL 相位在足够强的准周期调制下对“雪崩”是稳定的$d=2$, 和 (ii) 雪崩的可能性强烈限制了 MBL 过渡的有限尺寸缩放行为。我们提出了 MBL 不稳定的暗示性结构$d\ge 3$.