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arXiv · 2112.05066

Localization and fractality in disordered Russian Doll model

Vedant Motamarri·Alexander S. Gorsky·Ivan M. Khaymovich
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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.

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Vedant Motamarri, Alexander S. Gorsky, Ivan M. Khaymovich. 2021-12-09. Localization and fractality in disordered Russian Doll model. https://doi.org/10.21468/scipostphys.13.5.117

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