Algebraic integrability of the classical XXZ spin chain with reflecting boundary conditions

TL;DR

This paper demonstrates the algebraic integrability of the classical XXZ spin chain with reflecting boundaries by constructing explicit action-angle variables and integrating flows using Riemann theta functions.

Contribution

It introduces a system of log-canonical coordinates generalizing Sklyanin's separation of variables for this model, establishing its algebraic integrability.

Findings

Constructed log-canonical coordinates for the phase space.

Derived explicit action-angle variables for the system.

Integrated reflection Hamiltonian flows using Riemann theta functions.

Abstract

In this paper we analyze the classical XXZ spin chain with reflecting boundaries. We exhibit a system of log-canonical coordinates on the phase space generalizing Sklyanin's separation of variables for the periodic XXZ chain, and use these coordinates to construct action-angle variables for the system. We also integrate the flows of the reflection Hamiltonians explicitly in terms of Riemann theta functions. Central to our analysis is the algebraic integrability of the model.