Localization and fractality in disordered Russian Doll model
arXiv:2112.05066 · doi:10.21468/SciPostPhys.13.5.117
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.
arXiv comment18 pages, 6 figures, 49 references + 5 pages, 2 figures in Appendices
References in corpus (37)
- Anderson Transitions
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
- Anderson localization on the Bethe lattice: non-ergodicity of extended states
- A random matrix model with localization and ergodic transitions
- Integrability of the pairing hamiltonian
- Exact relations between multifractal exponents at the Anderson transition
- Correlation-induced localization
- Joint probability densities of level spacing ratios in random matrices
- Duality in power-law localization in disordered one-dimensional systems
- Dynamical phases in a "multifractal" Rosenzweig-Porter model
- Eigenfunction distribution for the Rosenzweig-Porter model
- Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
- Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
- The Lévy-Rosenzweig-Porter random matrix ensemble
- Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
- Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
- Multifractality without fine-tuning in a Floquet quasiperiodic chain
- Robustness of delocalization to the inclusion of soft constraints in long-range random models
- Higher order spacing ratios in random matrix theory and complex quantum systems
- Russian Doll Renormalization Group and Superconductivity
- Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model
- Emergent fractal phase in energy stratified random models
- On super-Poissonian behavior of the Rosenzweig-Porter model in the non-ergodic extended regime
- Non-ergodic delocalized phase with Poisson level statistics
- Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
- Integrals of motion for one-dimensional Anderson localized systems
- Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
- Chern-Simons theory and BCS superconductivity
- Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
- Integrability of the russian doll BCS model
- SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
- Anderson localization on a simplex
- Anisotropy-mediated reentrant localization
- Renormalization to localization without a small parameter
- Probing the metallic energy spectrum beyond the Thouless energy scale using the singular value decomposition