The su(N) XX model

TL;DR

This paper introduces and analyzes the integrable su(N) generalization of the XX model, establishing its properties, integrability, and spectrum, and discusses its potential application to an su(N) Hubbard model.

Contribution

It presents the first integrable su(N) XX model, constructs its R matrix, and diagonalizes its conserved laws using algebraic Bethe Ansatz, extending the known su(2) case.

Findings

The su(N) XX model is integrable with explicit R matrix.

The spectrum of the model is shown to be trivial.

Potential application to an su(N) Hubbard model is discussed.

Abstract

The natural su(N) generalization of the XX model is introduced and analyzed. It is defined in terms of the characterizing properties of the usual XX model: the existence of two infinite sequences of mutually commuting conservation laws and the existence of two infinite sequences of mastersymmetries. The integrability of these models, which cannot be obtained in a degenerate limit of the su(N)-XXZ model, is established in two ways: by exhibiting their R matrix and from a direct construction of the commuting conservation laws. We then diagonalize the conserved laws by the method of the algebraic Bethe Ansatz. The resulting spectrum is trivial in a certain sense; this provides another indication that the su(N) XX model is the natural generalization of the su(2) model. The application of these models to the construction of an integrable ladder, that is, an su(N) version of the Hubbard model, is mentioned.