• Corpus ID: 246867048

Domain Walls in the Heisenberg-Ising Spin-1/2 Chain

@inproceedings{Saenz2022DomainWI,
  title={Domain Walls in the Heisenberg-Ising Spin-1/2 Chain},
  author={Axel Saenz and Craig A. Tracy and Harold Widom},
  year={2022}
}

• A. Saenz, C. Tracy, H. Widom
• Published 15 February 2022
• Mathematics

In this paper we obtain formulas for the distribution of the left-most up-spin in the HeisenbergIsing spin-1/2 chain with anisotropy parameter ∆, also known as the XXZ spin-1/2 chain, on the one-dimensional lattice Z with domain wall initial conditions. We use the Bethe Ansatz to solve the Schrödinger equation and a recent antisymmetrization identity of Cantini, Colomo, and Pronko [9] to simplify the marginal distribution of the left-most up-spin. In the ∆ = 0 case, the distribution F2 arises. In the ∆ 6= 0 case, we propose a conjectural series expansion type formula based on a saddle point analysis. The conjectural formula turns out to be a Fredholm series expansion in the ∆ → 0 limit and recovers the result for ∆ = 0.