In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.

中文翻译：

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弱无序三维半金属的超对称层次模型

在本文中，我们研究了一类无间隙、三维、弱无序量子系统的分层超对称模型，在无序情况下显示点状费米面和能带的圆锥形交叉点。我们使用严格的重正化群方法和超对称性来计算系统的相关函数。我们证明了两点相关函数的代数衰减，与离域兼容。主要技术成分是通过迭代固定相展开对具有纯虚数协方差的无质量玻色高斯积分进行多尺度分析。