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

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