Dephasing Beyond the Markovian Limit; Implications for Many-Body Localization

Despite progress in understanding many-body localization (MBL) in one-dimension, many questions remain with respect to the nature of the transition and the stability of the MBL phase. We envision approaching the MBL transition from the high-temperature ergodic phase. We search for signatures of the transition as a failure of dephasing, which prevents the infrared divergence of quantum conductance corrections in the ergodic phase in 1D and 2D.
For an isolated fermion system with short-ranged interactions, dephasing is due to diffusive (strongly non-Markovian) thermal density fluctuations. A previous study identified a nontrivial RG fixed point in 4 – epsilon dimensions, at which the dephasing time diverges (Liao and Foster, PRL 2018). By contrast, long-range Coulomb interactions provide an approximately Markovian bath. A perfectly Markovian bath dephases at any nonzero temperature (Altshuler, Aronov, Khmelnitsky 1982).
We perturb about the exactly solvable Markovian limit, which we re-interpret as an exact, infinite-order diagrammatic summation. Using explicit calculations and scaling arguments, we will describe results beyond the Markovian limit in 1D and 2D.