## SciPost Submission Page

# Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

### by Sthitadhi Roy, David E. Logan

### Submission summary

As Contributors: | Sthitadhi Roy |

Arxiv Link: | https://arxiv.org/abs/1903.04851v1 |

Date submitted: | 2019-03-22 |

Submitted by: | Roy, Sthitadhi |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Condensed Matter Physics - Theory |

### Abstract

Many-body localisation is studied in a disordered quantum spin-1/2 chain with long-ranged power-law interactions, and distinct power-law exponents for interactions between longitudinal and transverse spin components. Using a self-consistent mean-field theory centring on the local propagator in Fock space and its associated self-energy, a localisation phase diagram is obtained as a function of the power-law exponents and the disorder strength of the random fields acting on longitudinal spin-components. Analytical results are corroborated using the well-studied and complementary numerical diagnostics of level statistics, entanglement entropy, and participation entropy, obtained via exact diagonalisation. We find that increasing the range of interactions between transverse spin components hinders localisation and enhances the critical disorder strength. In marked contrast, increasing the interaction range between longitudinal spin components is found to enhance localisation and lower the critical disorder.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-5-24 Invited Report

### Strengths

- analytical and numerical results

- clear explanations of the predicted phenomena

### Weaknesses

- it is hard to be convinced of the validity of the main results

### Report

This paper examine the possibility of MBL phases in systems with long range interactions at finite - infinite - temperature. There have been recent works on MBL phases in these systems but at small temperatures, working on Luttinger liquids. Here the authors find that increasing the range of longitudinal interactions in a spin system favour localisation, while increasing the traverse range (hopping terms) aids delocalisation. This behaviour can be somehow expected by general argument. Moreover they find critical value of the power law exponents for the decay of interactions below (and above) that system is always localised or always delocalised. Their findings are shown by numerical analysis of spectral statistics and mean field analytical results.

Few technical questions

- why the expectation value eq 17 for example can be taken only on zero magnetisation states? This is not the case in a infinite temperature state.

- eq 42 does reproduce the mean field result for W_c directly computed in the short range XXZ chain in the limit alpha and beta ->infinity? This would provide a more justification for validity of the method. Moreover it would be good to benchmark the result of the mean field approach with zero disorder cases, where other methods can be used.

- Is there a free fermion description of the Hamiltonian at some particular value of alpha, beta and J_z/J ?

Finally my main concern is the validity of the fully delocalised or fully localised phase. In the discussions there are numerous "appeal to continuity" namely it is assumed that a free system is continuos to an interacting (long ranged) system. There are no reasons to believe this "continuity". It is true that free systems under small disorder localise by Anderson transition but small long range interactions can break localisation even when these are infinitesimal. Is there a more solid argument to exclude such possibility?

### Requested changes

See report. Stronger arguments should be given for the transitions at critical alpha and beta.