## SciPost Submission Page

# Many-body localization in a quasiperiodic Fibonacci chain

### by Nicolas Macé, Nicolas Laflorencie, Fabien Alet

### Submission summary

As Contributors: | Fabien Alet · Nicolas Macé |

Arxiv Link: | https://arxiv.org/abs/1811.01912v3 |

Date accepted: | 2019-04-12 |

Date submitted: | 2019-03-28 |

Submitted by: | Macé, Nicolas |

Submitted to: | SciPost Physics |

Domain(s): | Theor. & Comp. |

Subject area: | Quantum Physics |

### Abstract

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.

###### Current status:

### Author comments upon resubmission

We thank the referees for careful reading our manuscript and the helpful comments/questions. We have replied to all referees' requests (detailed responses can be found in the comments to the reports). We additionally provide a full list of changes for completeness. We hope that after these improvements you will judge our manuscript suitable for publication.

### List of changes

1. The abstract now mentions the fact that the density distribution has extra peaks in the MBL Fibonacci phase.

2. The sentence on p. 2 has been replaced by "Finally, a discrete disorder distribution can also induce MBL, despite stronger finite size effects observed in the case of binary distributions".

3. On p. 4, the second paragraph of "Quasiperiodicity, samples of finite size and averaging over realizations" now includes a reference to the proof that Fibonacci sequences have L+1 words of length L.

4. We have expanded the discussion on the "large statistical errors" in a footnote on p. 4.

5. On p. 9-10, we have modified the text to make the explanation more understandable, leading with the analysis of Fig. 6 as suggested by the referee.

6. At the beginning of Sec. 5.3, we have expanded the introduction of the concept of participation entropy, detailing in particular the interpretation of the multifractal dimensions we ultimately compute.

7. We have rephrased the discussion of the fit in the MBL regime on p. 17 to make it clearer.

8. We have rewritten Sec. 5.3 to make it more careful, taking care not to make the claim of a new multifractal phase. We also added extra informations on the localisation of the orbitals at larger disorder.

9. We have clarified and enriched the discussion on entanglement growth in the free fermions model (Sec. 6.2).

10. We have clarified and added new details to the interacting chain dynamical exponent discussion (Sec. 6.2). We have also clarified the fitting procedure discussion (same Sec.).

11. We have expanded the discussion of the possible origin of the anomalous dynamical exponent (Sec. 6.2). We also added informations about the entanglement saturation value in the same section.

12. We have included the referee's remark about other deterministic geometries in the "Future directions" part.

13. We have made our statement about the free fermion's conductivity more precise (p. 5, Sec. 3).