科普：
https://www.quantamagazine.org/new-phys ... -20250815/
论文摘要：We consider a natural class of extensions of the Anderson model on Z, called random block Schrödinger operators (RBSOs), defined on the -dimensional torus ZZ. These operators take the form , where is a diagonal block matrix whose diagonal blocks are i.i.d. GUE, representing a random block potential, describes interactions between neighboring blocks, and is a small coupling parameter (making a perturbation of ). We focus on three specific RBSOs: (1) the block Anderson model, where is the discrete Laplacian on ZZ; (2) the Anderson orbital model, where is a block Laplacian operator; (3) the Wegner orbital model, where the nearest-neighbor blocks of are themselves random matrices. Assuming and for a small constant , and under a certain lower bound on , we establish delocalization and quantum unique ergodicity for bulk eigenvectors, along with quantum diffusion estimates for the Green's function. Combined with the localization results of arXiv:1608.02922, our results rigorously demonstrate the existence of an Anderson localization-delocalization transition for RBSOs as varies. Our proof is based on the -expansion method and the concept of self-energy renormalization, originally developed in the study of random band matrices in arXiv:2104.12048. In addition, we introduce a conceptually novel idea, called coupling renormalization, which extends the notion of self-energy renormalization. While this phenomenon is well-known in quantum field theory, it is identified here for the first time in the context of random Schrödinger operators. We expect that our methods can be extended to models with real or non-Gaussian block potentials, as well as more general forms of interactions.