2002/01/31 by F. C. Alcaraz, F C Alcaraz, Yu. G. Stroganov +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anisotropy #Ansatz #Bethe ansatz #Black Holes and Theoretical Physics #Boundary value problem #Ground state #Hamiltonian (control theory) #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Simple (philosophy) #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/0305-4470/35/17/301
published as J.Phys.A35:3805-3820,2002 · 19 pages, no figures
arxiv created 2002/04/03 · openalex publication_date 2002/04/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
From extensive numeric diagonalizations of the SU (3) Perk-Schultz Hamiltonian with a special value of the anisotropy and different boundary conditions, we have observed simple regularities for a significant part of its eigenspectrum. In particular, the ground-state energy and nearby excitations belong to this part of the spectrum. Our simple formulae describing these regularities recall, apart from some selection rules, the eigenspectrum of the free-fermion model. Based on the numerical observations we formulate several conjectures. Using explicit solutions of the associated nested Bethe-ansatz equations, guessed from an analysis of the functional equations of the model, we provide evidence for some of them.