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

by G. Z. Fehér, B. Pozsgay

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Submission summary

Authors (as registered SciPost users): Balázs Pozsgay
Submission information
Preprint Link:  (pdf)
Date accepted: 2019-05-21
Date submitted: 2019-05-09 02:00
Submitted by: Pozsgay, Balázs
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical


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.

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.

Published as SciPost Phys. 6, 063 (2019)

Reports on this Submission

Anonymous Report 1 on 2019-5-20 (Invited 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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