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

### Submission summary

 As Contributors: Balázs Pozsgay Arxiv Link: https://arxiv.org/abs/1808.06279v2 Date submitted: 2018-10-05 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 through a lattice path integral, which is evaluated exactly utilizing the so-called $F$-basis in the mirror (or quantum) channel. The final expression is similar to the Yudson representation of the infinite volume propagator, with the volume entering as a parameter. The contour integrals involve an amplitude describing the particular propagation process; this amplitude is similar to (but not identical with) the Bethe Ansatz wave function. An important feature is that it depends on two sets of coordinates (initial and final), and it is manifestly periodic for an arbitrary set of rapidities.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1808.06279v2 (5 October 2018)