Resonant energy scales and local observables in the many-body localized phase

Abstract

We formulate a theory for resonances in the many-body localized (MBL) phase of disordered quantum spin chains in terms of local observables. A key result is to show that there are universal correlations between the matrix elements of local observables and the many-body level spectrum. This reveals how the matrix elements encode the energy scales associated with resonance, thereby allowing us to show that these energies are power-law-distributed. Using these results, we calculate analytically the distributions of local polarizations and of eigenstate fidelity susceptibilities. The first of these quantities characterizes the proximity of MBL systems to noninteracting ones, while the second highlights their extreme sensitivity to local perturbations. Our theoretical approach is to consider the effect of varying a local field, which induces a parametric dynamics of spectral properties. We corroborate our results numerically using exact diagonalization in finite systems.