Localization and fractality in disordered Russian Doll model

TL;DR

This paper investigates the effects of disorder on the Russian Doll Model, revealing a fractal phase of non-ergodic delocalized states through a novel RG analysis, connecting localization, fractality, and integrability.

Contribution

It introduces a large-energy RG approach to analyze localization in the disordered Russian Doll Model, uncovering a unique fractal phase of non-ergodic delocalized states.

Findings

Discovery of a fractal phase with a distinct fractal dimension

Identification of non-ergodic delocalized states in the model

Development of a large-energy RG framework for spectral analysis

Abstract

Motivated by the interplay of Bethe-Ansatz integrability and localization in the Richardson model of superconductivity, we consider a time-reversal symmetry breaking deformation of this model, known as the Russian Doll Model (RDM), and implement diagonal on-site disorder. The localization and ergodicity-breaking properties of the single-particle spectrum are analyzed using a large-energy renormalization group (RG) over the momentum-space spectrum. Based on the above RG, we derive an effective Hamiltonian of the model, discover a fractal phase of non-ergodic delocalized states -- with the fractal dimension different from the paradigmatic Rosenzweig-Porter model -- and explain it in terms of the developed RG equations and the matrix-inversion trick.