1996/09/24 by J. Abad, Abad, J., Miguel Rios +2
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bethe ansatz #Chain (unit) #Condensed Matter (cond-mat) #Conjecture #Eigenvalues and eigenvectors #FOS: Physical sciences #Integrable system #Inverse problem #Inverse scattering problem #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Monodromy #Monodromy matrix #Physics #Pure mathematics #Quantum #Quantum inverse scattering method #Quantum many-body systems #Quantum mechanics #Representation (politics) #Space (punctuation) #TRACE (psycholinguistics) #Yang–Baxter equation #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9609228
Contribution presented in XXI Inter. Coll. on Group Theor. Methods, Goslar (1996), revtex, 4 figures
arxiv created 1996/09/24 · openalex publication_date 1996/09/24 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/08
The general expression for the local matrix L(θ) of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing L(θ) from the fundamental representation and imposing the fulfilment of the Yang-Baxter equation. Then, a non-homogeneous spin chain combining different representations of su(3) is solved by a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of su(n) is presented.