T–Q relation and exact solution for the XYZ chain with general non-diagonal boundary terms

2005/12/31 by Wen-Li Yang, Wen‐Li Yang, Yao-Zhong Zhang · 55 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Ansatz #Bethe ansatz #Boundary (topology) #Boundary value problem #Chain (unit) #Diagonal #Eigenvalues and eigenvectors #Geometry #Hamiltonian (control theory) #Integrable system #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Operator matrix #Physics #Quantum many-body systems #Quantum mechanics #Spectrum (functional analysis) #Transfer matrix #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2006.03.025

published in Nuclear Physics B 744(3), 312-329 (Elsevier BV) · Revtex4, 4 pages; V2, Latex file, 22 pages, the title is changed and new version contains the detailed derivations; V3, minor typos corrected, this version appears in Nucl. Phys. B

openalex publication_date 2006/04/07 · arxiv created 2006/05/11 · arxiv updated 2010/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We propose that the Baxter's Q-operator for the XYZ quantum spin chain with open boundary conditions is given by the j→ ∞ limit of the corresponding transfer matrix with spin-j (i.e., (2j+1)-dimensional) auxiliary space. The associated T-Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. This solution yields the complete spectrum of the Hamiltonian.

Citations

• A generalizedQ-operator forUqvertex models
• Integrable XYZ Spin Chain with Boundaries
• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. I. Some fundamental eigenvectors
• Row transfer matrix functional relations for Baxter's eight-vertex and six-vertex models with open boundaries via more general reflection matrices
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL
• Q-operator and T–Q relation from the fusion hierarchy
• Exact solution of Belavin model with open boundary condition
• Boundary conditions for integrable quantum systems
• Bethe ansatz solution of the openXXspin chain with non-diagonal boundary terms

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