Localization and fractality in disordered Russian Doll model

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