We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough qualitative level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus, we show that this MBL transition is in a universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $\nu \to \infty$, but the divergence is weaker than for the KT transition.

中文翻译：

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临界点附近的多体定位

我们检查一维量子系统中具有猝灭随机性和短程相互作用的多体定位（MBL）相变。在最近的工作之后，我们使用强随机重归一化组（RG）方法，其中相变是由于MBL相的雪崩不稳定性引起的。我们表明，可以在此RG中通过分析确定关键行为。在粗略的定性水平上，接近临界固定点的RG流动类似于先前显示的Kosterlitz-Thouless（KT）流动，但是临界行为之间存在重要差异。因此，我们证明此MBL转换属于与KT不同的通用性类。相关长度的差异对应于临界指数$\nu \to \infty$，但差异要比KT过渡弱。