Immunity of delocalization to soft constraints in long-range random models

P. A. Nosov, I. M. Khaymovich

Published 2019-04-25Version 1

Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with Pearson \green{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 immunity of states in the bulk of the spectrum to soft constraints is generally discussed for single-particle and many-body systems.