Many-body localization in the interpolating Aubry-Andr\'e-Fibonacci model

TL;DR

This paper explores how many-body localization in a spin chain is affected by a quasiperiodic potential interpolating between Aubry-Andre9 and Fibonacci models, revealing interaction-dependent localization transitions and anomalous effects.

Contribution

It introduces a model interpolating between two key quasiperiodic systems and analyzes how interactions influence localization, providing a detailed phase diagram with novel interaction effects.

Findings

Stronger interactions extend the ergodic phase in Aubry-Andre9 but shrink it in Fibonacci.

Localization transition points are continuously connected along the interpolation.

Weak interactions can localize the system, while stronger interactions promote ergodicity in certain regimes.

Abstract

We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbour coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-Andr\'e and the Fibonacci models. We find that stronger many-body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation. As a result, the position of the many-body localization transition depends on the interaction strength for an intermediate degree of deformation of the quasiperiodic modulation. Moreover, in the region of parameter space where the single-particle spectrum contains both localized and extended states, many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger interactions enhance ergodicity. We map the model's localization phase diagram using the decay of the quenched spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground for testing many-body localization under tunable potentials.