Quantum phases of quasiperiodic matter

Quasiperiodic systems offer a myriad of fascinating phenomena, from localization transitions in one or higher dimensions, to intriguing topological properties. There has been a continued interest in these systems due to their experimental accessibility across diverse platforms, including ultracold atoms and trapped ions, photonic and phononic media and, more recently, moiré materials. In this seminar, we will delve into our recent research on the quantum phases of both non-interacting and interacting quasiperiodic systems.

We will start by introducing a theoretical framework that we have developed to characterize the localization phase diagrams of non-interacting 1D quasiperiodic systems, that includes extended, localized, and even critical multifractal phases. This theory, based on a renormalization-group procedure, allowed us to connect widely different models in the literature and in some cases, fully analytically characterize the phase diagrams. We will then generalize our theory to interacting quasiperiodic systems.

By applying this generalization to a broad class of 1D quasiperiodic chains, we will unveil a compelling finding: short-range interactions become irrelevant in the vicinity of ground-state localization-delocalization transitions. Finally, we will explore the role of quasiperiodicity in moiré systems. Through illustrative examples, we will demonstrate that quasiperiodicity can be of crucial importance, being responsible for creating non-trivial states of matter, inaccessible in the periodic case.