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

### Submission summary

 As Contributors: Balázs Pozsgay Arxiv Link: https://arxiv.org/abs/1808.06279v4 Date accepted: 2019-05-21 Date submitted: 2019-05-09 Submitted by: Pozsgay, Balázs Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approach: Theoretical

### 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.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 6, 063 (2019)

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

Resubmission 1808.06279v4 on 9 May 2019
Resubmission 1808.06279v3 on 18 April 2019
Submission 1808.06279v2 on 5 October 2018

## Reports on this Submission

### Report

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

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