An algebraic approach to the Hubbard model

We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended SU(2 vertical bar 2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn. Crown Copyright (c) 2015 Published by Elsevier B.V. All rights reserved.