Robustness of delocalization to the inclusion of soft constraints in long-range random models

Abstract

Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the inclusion of the soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with Pearson correlation coefficient different from zero or unity. Counterintuitive robustness of delocalized phases, both ergodic and (multi)fractal, in these models is numerically observed and confirmed by the analytical calculations. First, matrix inversion trick is used to uncover the origin of such robustness. Next, to characterize delocalized phases a method of eigenstate calculation, sensitive to correlations in long-ranged hopping terms, is developed for random matrix models and approved by numerical calculations and previous analytical ansatz. The effect of the robustness of states in the bulk of the spectrum the inclusion of to soft constraints is generally discussed for single-particle and many-body systems.

10 pages, 5 figures, 94 references + 5 pages of Appendices

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• Flat-band-based multifractality in the all-band-flat diamond chain
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
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• Emergent multifractality in power-law decaying eigenstates
• Fractal states of the Schwinger model
• Robust extended states in Anderson model on partially disordered random regular graphs
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Excitation transfer in disordered spin chains with long-range exchange interactions
• Refined cyclic renormalization group in Russian Doll model
• Anderson localisation in spatially structured random graphs
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• Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking