## SciPost Submission Page

# The propagator of the finite XXZ spin-$\tfrac{1}{2}$ chain

### by G. Z. Fehér, B. Pozsgay

### Submission summary

As Contributors: | Balázs Pozsgay |

Arxiv Link: | https://arxiv.org/abs/1808.06279v4 |

Date submitted: | 2019-05-09 |

Submitted by: | Pozsgay, Balázs |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Quantum Physics |

### Abstract

We derive contour integral formulas for the real space propagator of the spin-$\tfrac12$ XXZ chain. The exact results are valid in any finite volume with periodic boundary conditions, and for any value of the anisotropy parameter. The integrals are on fixed contours, that are independent of the Bethe Ansatz solution of the model and the string hypothesis. The propagator is obtained by two different methods. First we compute it through the spectral sum of a deformed model, and as a by-product we also compute the propagator of the XXZ chain perturbed by a Dzyaloshinskii-Moriya interaction term. As a second way we also compute the propagator through a lattice path integral, which is evaluated exactly utilizing the so-called $F$-basis in the mirror (or quantum) channel. The final expressions are similar to the Yudson representation of the infinite volume propagator, with the volume entering as a parameter. As an application of the propagator we compute the Loschmidt amplitude for the quantum quench from a domain wall state.

###### Current status:

### Author comments upon resubmission

We are thankful to the referee for the comments, we implemented the requests.

### List of changes

1. We added all the requested references. (in the case of the DM interaction term we only added the paper dealing with the XXZ case)

2. We added a criticial discussion in the Conclusions, this is the last paragraph.

3. We added an acknowledgement of the useful help of the referee. Indeed this is appropriate in the present case, we should have added this already in the last version.

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-5-20 Invited Report

### Report

All suggested corrections have been made, and I think that the paper is now in a suitable form to be published.