We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent ν. This class includes disordered systems with intrinsic- or symmetry-protected- topological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement (an entanglement entropy with a scaling intermediate between area and volume law). We investigate the stability of marginal localization in the presence of interactions, and argue that arbitrarily weak short range interactions trigger delocalization for partially filled bands at non-zero energy density if ν\ge 1/d. We use the Harris/Chayes bound ν\ge 2/d, to conclude that marginal localization is generically unstable in the presence of interactions. Our results suggest the impossibility of stabilizing quantized Hall conductance at non-zero energy density.
Effective delocalization in the one-dimensional Anderson model with stealthy disorder
Princeton University（普林斯顿大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）；Columbia University（哥伦比亚大学）
Eigenstate transitions and critical transport in 3D Aubry-André model
J. Stefan Institute（约热·斯蒂芬研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；Institute of Theoretical Physics, Wroclaw University of Science and Technology（弗罗茨瓦夫科技大学理论物理研究所）
