Quantum dynamics in the interacting Fibonacci chain

Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultracold atom experiments where nontrivial localized phases have been observed. One such quasiperiodic model is the so-called Fibonacci model. In this tight-binding model, noninteracting 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 noninteracting 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.

Automated summary

The study investigates whether anomalous diffusion in the noninteracting Fibonacci model persists in the presence of interactions and establishes connections to a possible transition towards a localized phase. This is done by studying real-time spread of density-density correlations, calculating the participation entropy in configuration space, and investigating the expectation value of local observables in the diagonal ensemble to corroborate the findings.