Completeness of states of the generalized Heisenberg magnet

DOI10.1007/BF01104977zbMath0613.58014MaRDI QIDQ1819429

Anatol N. Kirillov

Publication date: 1987

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

characterirreducible representationsBethe modelgeneralized Heisenberg magnetic model

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Statistical mechanics of solids (82D20) Geometric quantization (53D50)

Related Items (19)

Completeness of Wronskian Bethe equations for rational \(\mathfrak{gl}_{\mathsf{m}|\mathsf{n}}\) spin chains ⋮ Unnamed Item ⋮ T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model ⋮ Completeness of Bethe ansatz for 1D Hubbard model with ab-flux through combinatorial formulas and exact enumeration of eigenstates ⋮ Free energy and excitation spectrum over ferromagnetic ground state for even spin Fateev-Zamolodchikov model ⋮ Classification and completeness of Bethe states and excitation spectrum for the spin \(4\) Fateev-Zamolodchikov model. ⋮ Existence of crystal bases for Kirillov-Reshetikhin modules of type \(D\) ⋮ On completeness of Bethe Ansatz solutions for sl(2) Richardson–Gaudin systems ⋮ The expansion of immaculate functions in the ribbon basis ⋮ A Bethe Ansatz study of free energy and excitation spectrum for even spin Fateev–Zamolodchikov model ⋮ String hypothesis for \({{\mathfrak{g}\mathfrak{l} (\mathfrak{n} | \mathfrak{m})}}\) spin chains: a particle/hole democracy ⋮ Integrability and exact solution for coupled BCS systems associated with the \(\mathrm{su}(4)\) Lie algebra ⋮ Plücker relations on Schur functions ⋮ Spectrum and completeness of the three-state superintegrable chiral Potts model ⋮ Physical combinatorics and quasiparticles ⋮ Algebraic properties of an integrable \(t\)-\(J\) model with impurities ⋮ Quantum matrix algebras of the \(\text{GL}(m|n)\) type: the structure and spectral parameterization of the characteristic subalgebra ⋮ Generalization of the Gale-Ryser theorem ⋮ The Bethe equation at \(q=0\), the Möbius inversion formula, and weight multiplicities. II: The \(X_n\) case

Cites Work

• Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model
• Quantum inverse problem method. I
• Diagonalisation of GL(N) invariant transfer matrices and quantum N-wave system (Lee model)
• Unnamed Item
• Unnamed Item
• Unnamed Item

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