Does localization occur in a hierarchical random-matrix model for many-body states?

Abstract

We use random-matrix theory and supersymmetry techniques to work out the two-point correlation function between states in a hierarchical model which employs Feshbach's chaining hypothesis: Classes of many-body states are introduced. Only states within the same or neighboring classes are coupled. We assume that the density of states per class grows monotonically with class index. The problem is mapped onto a one-dimensional non-linear sigma model. In the limit of a large number of states in each class we derive the critical exponent for the growth of the level density with class index for which delocalization sets in. From a realistic modelling of the class-dependence of the level density, we conclude that the model does not predict Fock-space localization in nuclei.