Interaction instability of localization in quasiperiodic systems

Abstract

<p id="d1827964e139">Understanding how small imperfections affect a system’s dynamics is one of the central questions of theoretical physics—namely, do properties change in a smooth way, such that small perturbation leads to small changes, or do they change discontinuously? Localization in disordered many-particle quantum systems has been shown to be stable to interactions. On a single-particle level, one can also achieve localization with a quasiperiodic potential—a system without disorder but with rich properties. It is believed that localization in disordered as well as in quasiperiodic potentials behaves in essentially the same way, in particular, that both are stable against interactions. We show that this is not so. A quasiperiodic localized system discontinuously changes from localization to diffusion upon introducing interactions. </p><p class="first" id="d1827964e142">Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites. </p>