## SciPost Submission Page

# Detecting a many-body mobility edge with quantum quenches

### by Piero Naldesi, Elisa Ercolessi, Tommaso Roscilde

#### - Published as SciPost Phys. 1, 010 (2016)

### Submission summary

As Contributors: | Piero Naldesi · Tommaso Roscilde |

Arxiv Link: | http://arxiv.org/abs/1607.01285v3 |

Date accepted: | 2016-10-27 |

Date submitted: | 2016-10-21 |

Submitted by: | Roscilde, Tommaso |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approaches: | Theoretical, Computational |

### Abstract

The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to "localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

### Ontology / Topics

See full Ontology or Topics database.Published as SciPost Phys. 1, 010 (2016)

### List of changes

The criterion for the estimate of the MBL-extended transition region from the scaling of the adjacent gap ratio is thoroughly discussed and implemented in section 3.1. A sentence is added in the conclusions concerning the possible experimental signatures. Fig. 4 has been added, the newly obtained estimates of the transition from the adjacent-gap ratio are reported in Fig. 3, and an updated gray-shaded area -- marking the transition -- appears now in the modified version of Figs. 5, 6, 7, 9, 11.

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2016-10-21 Invited Report

- Cite as: Anonymous, Report on arXiv:1607.01285v3, delivered 2016-10-21, doi: 10.21468/SciPost.Report.30

### Strengths

See previous report

### Weaknesses

See previous report, the authors have satisfactorily addressed these points.

### Report

With the revisions implemented in the new version, the authors have, in my opinion, satisfactorily addressed both Referees' comments. I recommend the publication of this very nice ,well written and relevant publication as is.

Just two clarifications/comments on the authors' response (with no intention to

trigger additional revisions):

Ad 5) An inverted mobility edge was predicted by Altshuler et al. in Phys. Rev. Lett. 113, 045304. Moreover a 2D Bose-Hubbard model with disorder at for the parameters of Ref. 14, is in a superfluid state at T=0 (see work by Svistunov, Prokoviev, Pollet and others). Given that this experiment seems to observe many-body localization at higher energy densities, such an inverted mobility edge could exist.

Ad 7) Here I primarily wanted to point out that while there is ample evidence

for subdiffusive dynamics in a portion of the ergodic phase (be it based on

equilibrium or far from equilibrium probes), there is nevertheless an inconsistent picture when it comes to computing the conductivity itself.

I disagree with the authors' perception of the role of baths in the calculation of conductivities. As far as I understand, conductivities are bulk properties and transport is an intrinsic property, the bath just provides temperature and perhaps other control parameters to define the appropriate equilibrium ensemble, but it is (in the present context) not the source of conducting behavior per se.

In linear response, the claim of subdiffusive dynamics and a finite dc conductivity seem irreconcilable to me. Recall that the very phenomenological definition of the many-body localized phase goes via sigma_dc=0 (computed in a thermal ensemble!), see Basko, Aleiner and Altshuler.

~

### Requested changes

1- The authors could perhaps update Refs. 14,15, & 55, which

in the meantime all were published.