## SciPost Submission Page

# Generalized hydrodynamics regime from the thermodynamic bootstrap program

### by Axel Cortés Cubero, Miłosz Panfil

### Submission summary

As Contributors: | Milosz Panfil |

Arxiv Link: | https://arxiv.org/abs/1909.08393v3 |

Date submitted: | 2019-11-28 |

Submitted by: | Panfil, Milosz |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### Abstract

Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field theories, we show the same correlators can be computed as a sum over form factors, the GHD regime corresponding to the leading contribution with one particle-hole pair on a finite energy-density background. The thermodynamic bootstrap program (TBP) formalism was recently introduced as an axiomatic approach to computing such finite-energy-density form factors for integrable field theories. We derive a new axiom within the TBP formalism from which we easily recover the predicted GHD Eulerian correlators. We also compute higher form factor contributions, with more particle-hole pairs, within the TBP, allowing for the computation of correlation functions in the diffusive, and beyond, GHD regimes. The two particle-hole form factors agree with expressions recently conjectured within the~GHD.

###### Current status:

### Author comments upon resubmission

Please find our resubmission of the manuscript to the SciPost Physics.

We have addressed all the points raised by the referees and added a discussion on the in-cell averaging.

Kind regards,

the authors

### List of changes

The main changes are:

1) we have improved notation in the introduction, as requested by the referee 1 and 3;

2) we have provided computations showing that higher particle form factors do not contribute to the correlator at the Eulerian scale (section 6);

3) we have clarified the terminology (dressed form factors, section 3) and added a discussion how the newly derived formula fits within the bootstrap program (end of section 4);

4) we have clarified the notation in the analysis of non-analyticities of form-factors in section 5;

5) we have added a comment that similarity between finite temperature and finite size form-factors was previously observed for Ising field theory (end of section 4);

6) finally, we have included the in-cell averaging procedure in the derivation of the Eulerian scale correlators in section 6. This procedure is needed to fully recover the Eulerian-scale predictions of the GHD. This step of the derivation was missing in the first submission.

### Submission & Refereeing History

- Report 2 submitted on 2019-12-09 11:18 by
*Anonymous* - Report 1 submitted on 2019-12-04 10:22 by
*Anonymous*

## Reports on this Submission

### Anonymous Report 2 on 2019-12-9 Invited Report

### Report

All appropriate changes have been and I think the paper can be published now.

### Anonymous Report 1 on 2019-12-4 Invited Report

### Report

I thank the authors for answering my points, and recommend the paper in its current version for publication.