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

TL;DR

This paper introduces a general method for transforming integrable spin chains into open chains with boundaries, demonstrated on the Heisenberg XXX and Inozemtsev models, preserving integrability via Yangian symmetries.

Contribution

A novel 'bottom-up' approach to construct integrable boundary conditions for spin chains, applicable to various models including long-range interactions.

Findings

New boundary Hamiltonians with Yangian symmetry

Method successfully applied to Heisenberg XXX and Inozemtsev models

Ensures integrability of open spin chains with boundaries

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.