How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models

Abstract

We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a "bottom-up" approach for constructing integrable boundaries and can be applied to any spin chain model.

9 pages, 1 figure; v.2 references added. Accepted to Phys. Lett. A

References in corpus (4)

• Symmetries of Spin Calogero Models
• The particle-hole transformation, supersymmetry and achiral boundaries of the open Hubbard model
• Twisted Yangians and symmetric pairs
• Twisted Yangian symmetry of the open Hubbard model

Cited by in corpus (1)

• How coordinate Bethe ansatz works for Inozemtsev model