Many Body Localization Transition in Quasiperiodic Systems

We study the many body localization transition in an XXZ spin chain subject to a quasiperiodic field by examining the structure of the local conserved quantities (l-bits) in the phase diagram. We construct l-bits by evolving local operators by the Hamiltonian and averaging over time. Motivated by the non-interacting transition that occurs in this model, we consider the weight of the l-bit on two body fermion operators and show that this two body weight contains the dominate contributions to the l-bit in the thermal phase. Further, we show that these contributions arise from hydrodynamic modes in the model. By subtracting the projection onto the hydrodynamic modes from the l-bits, we obtain a quantity that is sensitive to the localization transition. We find that the transition occurs at stronger quasiperiodic modulations and has a larger critical exponent than previously estimated, while other estimates are affected by strong finite size effects.