1996/10/25 by Frank Göhmann, Shuichi Murakami · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Eigenvalues and eigenvectors #Fermion #Hubbard model #Invariant (physics) #Lie algebra #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Monodromy #Monodromy matrix #Nonlinear Waves and Solitons #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum mechanics #Transfer matrix #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/30/15/014
published as J.Phys.A:Math.Gen.30(1997)5269-5287 · 30 pages, LaTeX, no figures, paragraph added in the appendix
arxiv created 1996/10/25 · openalex publication_date 1997/08/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We reconsider the quantum inverse scattering approach to the one-dimensional Hubbard model and work out some of its basic features so far omitted in the literature. It is our aim to show that the R-matrix and monodromy matrix of the Hubbard model, which have now been known for ten years, have good elementary properties. We provide a meromorphic parametrization of the transfer matrix in terms of elliptic functions. We identify the momentum operator for lattice fermions in the expansion of the transfer matrix with respect to the spectral parameter and thereby show the locality and translational invariance of all higher conserved quantities. We work out the transformation properties of the monodromy matrix under the su(2) Lie algebra of rotations and under the -pairing su(2) Lie algebra. Our results imply invariance of the transfer matrix for the model on a chain with an even number of sites.