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

TL;DR

This paper explores how singular continuous energy spectra in interacting many-body systems lead to anomalous slow dynamics, emphasizing the role of many-body correlations beyond mean-field approximations.

Contribution

It demonstrates the presence of singular-continuous spectra in interacting systems and links this to anomalous dynamics, highlighting the importance of many-body correlations.

Findings

Singular-continuous spectra can exist in interacting many-body systems.

Anomalous slowing down of dynamics is linked to the spectral properties.

Many-body correlations are crucial for the emergence of anomalous behavior.

Abstract

We investigate the dynamical properties of an interacting many-body system with a non-trivial 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 presence of interaction has recently been 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 non-trivial interplay between geometry and interactions.