Integrals of motion in the Many-Body localized phase

Understand

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.