2014/06/30 by V. Ros, M. Mueller, A. Scardicchio · 1 citation
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.nuclphysb.2014.12.014
published as Nuclear Physics, Section B (2015), pp. 420-465 · 65 pages, 12 figures. Corrected typos, added references
arxiv created 2015/01/02 · arxiv updated 2015/01/05
We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum \0,1\, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.