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Many-body localization (MBL), characterized by the absence of thermalizationand the violation of conventional thermodynamics, has elicited much interestboth as a fundamental physical phenomenon and for practical applications inquantum information. A phenomenological model, which describes the system usinga complete set of local integrals of motion (LIOMs), provides a powerful toolto understand MBL, but can be usually only computed approximately. Here weexplicitly compute a complete set of LIOMs with a non-perturbative approach, bymaximizing the overlap between LIOMs and physical spin operators in real space.The set of LIOMs satisfies the desired exponential decay of weight of LIOMs inreal-space. This LIOM construction enables a direct mapping from the real spaceHamiltonian to the phenomenological model and thus enables studying thelocalized Hamiltonian and the system dynamics. We can thus study and comparethe localization lengths extracted from the LIOM weights, their interactions,and dephasing dynamics, revealing interesting aspects of many-bodylocalization. Our scheme is immune to accidental resonances and can be appliedeven at phase transition point, providing a novel tool to study the microscopicfeatures of the phenomenological model of MBL.

Comparing many-body localization lengths via non-perturbative construction of local integrals of motion