Slow scrambling in disordered quantum systems

In this work we study the effect of static disorder on the growth of commutators—a probe of information scrambling in quantum many-body systems—in a variety of contexts. We find generically that disorder slows the onset of scrambling and, in the case of a many-body localized (MBL) state, partially halts it. In the MBL state, we show using a fixed point Hamiltonian that operators exhibit slow logarithmic growth under time evolution and compare the result with the expected growth of commutators in (de)localized noninteracting disordered models. Finally, using a scaling argument, we state a conjecture on the growth of commutators in a weakly interacting diffusive metal.