Boundary K-matrices for the XYZ, XXZ AND XXX spin chains

TL;DR

This paper derives general solutions for boundary reflection matrices in XYZ, XXZ, and XXX spin chains, explicitly constructing associated integrable Hamiltonians with parameter families.

Contribution

It provides the first comprehensive solutions for boundary K-matrices in these models, including explicit Hamiltonian derivations with continuous and discrete parameters.

Findings

Explicit solutions for reflection matrices in XYZ, XXZ, and XXX models.

Derivation of integrable Hamiltonians with parameter families.

Identification of continuous and discrete parameter dependencies.

Abstract

The general solutions for the factorization equations of the reflection matrices $K^{\pm}(\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are explicitly derived, finding families dependig on several continuous as well as discrete parameters.