Quantum dynamics in the interacting Fibonacci chain

TL;DR

This paper explores how interactions affect quantum dynamics in the Fibonacci quasiperiodic model, examining whether anomalous diffusion persists and identifying potential localization transitions through numerical simulations.

Contribution

It is the first study to analyze the impact of interactions on quantum transport and localization in the Fibonacci model using real-time dynamics and entropy measures.

Findings

Anomalous diffusion persists in the interacting Fibonacci model.

Interactions can induce a transition towards localization.

Real-time correlation spreading shows signatures of a phase transition.

Abstract

Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultra-cold atom experiments where non trivial localised phases have been observed. One such quasiperiodic model is the so called Fibonacci model. In this tight-binding model, non-interacting particles are subject to on-site energies generated by a Fibonacci sequence. This is known to induce critical states, with a continuously varying dynamical exponent, leading to anomalous transport. In this work, we investigate whether anomalous diffusion present in the non-interacting system survives in the presence of interactions and establish connections to a possible transition towards a localized phase. We investigate the dynamics of the interacting Fibonacci model by studying real-time spread of density-density correlations at infinite temperature using the dynamical typicality approach. We also corroborate our findings by calculating the participation entropy in configuration space and investigating the expectation value of local observables in the diagonal ensemble.