# Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model

### Submission summary

 As Contributors: Jerome Dubail · Stefano Scopa Preprint link: scipost_202109_00036v2 Date accepted: 2022-06-13 Date submitted: 2022-01-10 19:58 Submitted by: Scopa, Stefano Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|\Delta|< 1$, initially prepared in a product state with two domain walls i.e, $|\downarrow\dots\downarrow\uparrow\dots\uparrow\downarrow\dots\downarrow\rangle$. At early times, the two domain walls evolve independently and only after a calculable time a non-trivial interplay between the two emerges and results in the occurrence of a split Fermi sea. For $\Delta=0$, we derive exact asymptotic results for the magnetization and the spin current by using a semi-classical Wigner function approach, and we exactly determine the spreading of entanglement entropy exploiting the recently developed tools of quantum fluctuating hydrodynamics. In the interacting case, we analytically solve the Generalized Hydrodynamics equation providing exact expressions for the conserved quantities. We display some numerical results for the entanglement entropy also in the interacting case and we propose a conjecture for its asymptotic value.

Published as SciPost Phys. 12, 207 (2022)

Dear Editor(s),

We thank you for considering our manuscript “Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model” for publication in SciPost.
We are pleased to see a positive feedback on our results from both the referees. You can find attached a point-by-point response to the referees reports and a list of changes in the revised version of the manuscript. Changes in the text are highlighted to help the review process.
However, we disagree with the fact that our manuscript does not meet the criteria for publication in SciPost Physics and has been downgraded to SciPost Physics Core. On the basis of the very positive referees reports for SciPost Physics, the motivations for this downgrade are obscure to us.
We then resubmit the manuscript to SciPost Physics being confident that this revised version of the manuscript can meet its acceptance criteria.

Sincerely,

The authors.

### List of changes

We list below the changes that we made on the revised version of the manuscript (changes are highlighted in the text.)
1) We modified the layout of our manuscript using the template of SciPost journals.
2) We modified some sentences in Sec. 1 according to the comment of the referee 1.
3) We inserted Ref. [45].
4) We added a sentence in Sec. 3.1 below Eq. (13) according to the comment of the referee 1.
5) We corrected small typos in the text, including those mentioned by referee 1.