Emergence of anomalous dynamics from the underlying singular continuous spectrum in interacting many-body systems

Abstract

We investigate the dynamical properties of an interacting many-body system with a nontrivial energy potential landscape that may induce a singular continuous single-particle energy spectrum. Focusing on the Aubry-Andr\'e model, whose anomalous transport properties in the presence of interaction was recently demonstrated experimentally in an ultracold-gas setup, we discuss the anomalous slowing down of the dynamics it exhibits and show that it emerges from the singular-continuous nature of the single-particle excitation spectrum. Our study demonstrates that singular-continuous spectra can be found in interacting systems, unlike previously conjectured by treating the interactions in the mean-field approximation. This, in turns, also highlights the importance of the many-body correlations in giving rise to anomalous dynamics, which, in many-body systems, can result from a nontrivial interplay between geometry and interactions.