Many-Body-Localization : Strong Disorder perturbative approach for the Local Integrals of Motion

For random quantum spin models, the strong disorder perturbative expansion of the Local Integrals of Motion (LIOMs) around the real-spin operators is revisited. The emphasis is on the links with other properties of the Many-Body-Localized phase, in particular the memory in the dynamics of the local magnetizations and the statistics of matrix elements of local operators in the eigenstate basis. Finally, this approach is applied to analyze the Many-Body-Localization transition in a toy model studied previously from the point of view of the entanglement entropy.