Avoiding Ergodicity: Localization in Clean Interacting Systems

Since the phenomenon of many-body-localization (MBL) was re-postulated more than a decade ago, it has attracted a great deal of attention. A key ingredient for achieving the MBL phase is disorder (randomness). The roots of this phase lie within the phenomenon of Anderson localization, where non-interacting particles form a localized non-ergodic phase. It is the question regarding the fate of Anderson localization in the presence of interactions that plants the seed
for the discovery of the MBL phase.
We wish to go beyond the conventional paradigm and ask whether randomness is indeed an essential ingredient
in achieving generic non-ergodic interacting phases.
We proposed the idea that the essential ingredient for MBL is localization, which does not necessarily
mean disorder. We analyze the spectral and the dynamical properties of one-dimensional interacting fermions and spins in the presence of both disorder and linear potential. We show that by considering these two different localizing mechanisms, i.e., disorder and linear fields, one may construct a two-dimensional phase diagram which hosts a connected non-ergodic (MBL) phase.