Integrable $1/r^2$ Spin Chain with Reflecting End

TL;DR

This paper introduces a new integrable spin chain model of the Haldane-Shastry type with a reflecting end, characterized by lattice points related to Laguerre polynomial zeros, and explicitly constructs its integrals of motion.

Contribution

It presents a novel integrable spin chain with a reflecting boundary, expanding the class of exactly solvable models in quantum integrable systems.

Findings

The model is integrable and of Haldane-Shastry type.

Lattice points are related to zeros of Laguerre polynomials.

Explicit construction of integrals of motion is provided.

Abstract

A new integrable spin chain of the Haldane-Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a {\it reflecting end}. The lattice points of this model consist of the square roots of the zeros of the Laguerre polynomial. Using the ``exchange operator formalism'', the integrals of motion for the model are explicitly constructed.