Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2006-10-09
J.Stat.Mech.0701:P01017,2007
Nonlinear Sciences
Exactly Solvable and Integrable Systems
66 pages, v2: minor changes, references added, to appear in JSTAT
Scientific paper
10.1088/1742-5468/2007/01/P01017
We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2,2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su(2|2). These results are applied in the construction and investigation of an interesting S-matrix with su(2|2) symmetry. In particular, they enable a remarkably simple proof of the Yang-Baxter relation. We also show the equivalence of the S-matrix to Shastry's R-matrix and thus uncover a hidden supersymmetry in the integrable structure of the Hubbard model. We then construct eigenvalues of the corresponding transfer matrix in order to formulate an analytic Bethe ansatz. Finally, the form of transfer matrix eigenvalues for models with psu(2,2|4) symmetry is sketched.
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