高维非常规局域化跃迁
Unconventional localisation transition in high dimensions
摘要：
研究了具有幂律准粒子色散$ξ_{\bf k}\propto k^α$和随机短程关联势的非相互作用系统。我们表明，与较低的维度的情况下，对于$d>2α$存在一个临界无序强度（设置的带宽），在该系统表现出无序驱动的量子相变在底部的频带，在于从安德森过渡的普适性类。与传统智慧相反，它表现在，例如，无序平均态密度对于允许局部化的对称类系统，这种转变的显著特征是流动性边缘的非分析行为，即被钉在亚临界无序带的底部，并在无序超过临界强度时增长。专注于状态的密度，我们计算的临界行为（指数和标度函数）在这个新的过渡，使用重整化组，由$\varepsilon=2α-d$扩展控制。我们还将我们的分析应用于狄拉克材料，例如，外尔半金属，这种转变发生在物理上有趣的三维空间。
英文摘要：
We study non-interacting systems with a power-law quasiparticle dispersion $ξ_{\bf k}\propto k^α$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2α$ there exists a critical disorder strength (set by the band width), at which the system exhibits a disorder-driven quantum phase transition at the bottom of the band, that lies in a universality class distinct from the Anderson transition. In contrast to the conventional wisdom, it manifests itself in, e.g., the disorder-averaged density of states. For systems in symmetry classes that permit localisation, the striking signature of this transition is a non-analytic behaviour of the mobility edge, that is pinned to the bottom of the band for subcritical disorder and grows for disorder exceeding a critical strength. Focussing on the density of states, we calculate the critical behaviour (exponents and scaling functions) at this novel transition, using a renormalisation group, controlled by an $\varepsilon=2α-d$ expansion. We also apply our analysis to Dirac materials, e.g., Weyl semimetal, where this transition takes place in physically interesting three dimensions.
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