4.5 Article

Localization and fractality in disordered Russian Doll model

Journal

SCIPOST PHYSICS
Volume 13, Issue 5, Pages -

Publisher

SCIPOST FOUNDATION
DOI: 10.21468/SciPostPhys.13.5.117

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Motivated by the interplay of Bethe-Ansatz integrability and localization in the Richardson model of superconductivity, this study analyzes the localization and ergodicity-breaking properties of the single-particle spectrum in a time-reversal symmetry breaking deformation known as the Russian Doll Model (RDM) with diagonal on-site disorder. A large-energy renormalization group (RG) method is used to derive an effective Hamiltonian for the model and a fractal phase of non-ergodic delocalized states is discovered, with a fractal dimension different from the Rosenzweig-Porter model.
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.

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