Localization and fractality in disordered Russian Doll model

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.

18 pages, 6 figures, 49 references + 5 pages, 2 figures in Appendices

References in corpus (14)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Exact relations between multifractal exponents at the Anderson transition
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• The Lévy-Rosenzweig-Porter random matrix ensemble
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• Anderson localization on a simplex
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