Exact Solution of Long-Range Interacting Spin Chains with Boundaries

TL;DR

This paper provides an exact analytical solution for long-range interacting spin chains with boundaries, revealing their spectral properties and symmetries through a novel mapping to Calogero-Sutherland models.

Contribution

It introduces a method to solve boundary Haldane-Shastry type models exactly by connecting them to BC-type Calogero-Sutherland systems.

Findings

Derived the spectrum of boundary Haldane-Shastry models.

Identified the highest weight eigenstates.

Established the symmetry structure via reflection equations.

Abstract

We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models. Using a map to the Calogero-Sutherland Hamiltonian of BC type, we derive the spectrum and the highest weight eigenstates.