Localization and fractality in disordered Russian Doll model

Motamarri , Vedant R.; Gorsky, Alexander S.; Khaymovich, Ivan M.

doi:10.21468/SciPostPhys.13.5.117

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Localization and fractality in disordered Russian Doll model

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Khaymovich, Ivan M.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Motamarri, V. R., Gorsky, A. S., & Khaymovich, I. M. (2022). Localization and fractality in disordered Russian Doll model. SciPost Physics Core, 13(5): 117. doi:10.21468/SciPostPhys.13.5.117.

Cite as: https://hdl.handle.net/21.11116/0000-000C-B9DA-E

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.