New boundary conditions for integrable lattices

TL;DR

This paper introduces new boundary conditions for integrable nonlinear lattices of the XXX type, expanding the class of solvable models and connecting them to Calogero-Moser systems through algebraic structures.

Contribution

It formulates integrable boundary conditions for XXX lattices using a general rank 1 ansatz, linking these to dynamical symmetries of Calogero-Moser problems.

Findings

New boundary conditions for XXX lattices are constructed.

The quadratic algebra relates to Calogero-Moser dynamical symmetry.

Physical realizations of the algebra are discussed.

Abstract

New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting with two additional spins at each end of the chain. The construction uses the most general rank 1 ansatz for the 2x2 L-operator satisfying the reflection equation algebra with rational r-matrix. The associated quadratic algebra is shown to be the one of dynamical symmetry for the A1 and BC2 Calogero-Moser problems. Other physical realizations of our quadratic algebra are also considered.