Many-body localization in a multifractal fermionic chain*

We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a deterministic quasiperiodic on-site potential following the Fibonacci sequence. With this choice, the single-particle eigenstates are delocalized and multifractal, no matter how strong the potential is.

Contrary to naive expectations, adding interactions in this system does not enhance delocalization, and a MBL transition is observed. Due to the highly correlated nature of the potential, the MBL phase presents features which differ from those encountered for the more documented random-box potential. We observe for example extra peaks in the fermion density distribution which we can relate to the occurrence of specific local patterns in the quasiperiodic potential.
Furthermore, in the ergodic phase, non-trivial proprerties of the single-particle density matrix are observed, compatible with a persistence of the free fermions multifractality.
Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.