Many-body localization in a quasiperiodic Fibonacci chain

We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.

MULTIFRACTALITY IN THE GENERALIZED AUBRY–ANDRÉ QUASIPERIODIC LOCALIZATION MODEL WITH POWER-LAW HOPPINGS OR POWER-LAW FOURIER COEFFICIENTS

The nearest-neighbor Aubry–André quasiperiodic localization model is generalized to include power-law translation-invariant hoppings [Formula: see text] or power-law Fourier coefficients [Formula: see text] in the quasiperiodic potential. The Aubry–André duality between [Formula: see text] and [Formula: see text] manifests when the Hamiltonian is written in the real-space basis and in the Fourier basis on a finite ring. The perturbative analysis in the amplitude [Formula: see text] of the hoppings yields that the eigenstates remain power-law localized in real space for [Formula: see text] and are critical for [Formula: see text] where they follow the strong multifractality linear spectrum, as in the equivalent model with random disorder. The perturbative analysis in the amplitude [Formula: see text] of the quasiperiodic potential yields that the eigenstates remain delocalized in real space (power-law localized in Fourier space) for [Formula: see text] and are critical for [Formula: see text] where they follow the weak multifractality Gaussian spectrum in real space (or strong multifractality linear spectrum in the Fourier basis). This critical case [Formula: see text] for the Fourier coefficients [Formula: see text] corresponds to a periodic function with discontinuities, instead of the cosinus function of the standard self-dual Aubry–André model.

Interaction instability of localization in quasiperiodic systems

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.