2010/05/31 by Luigi Amico, Holger Frahm, Andreas Osterloh +1 · 65 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Bethe ansatz #Boson #Boundary value problem #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Integrable system #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Physics #Polynomial #Pure mathematics #Quantum mechanics #Separation of variables #Spectrum (functional analysis) #Transfer matrix #cond-mat.other #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1016/j.nuclphysb.2010.07.005
published in Nuclear Physics B 839(3), 604-626 (Elsevier BV) · 30 pages, revtex4. Minor changes
openalex publication_date 2010/07/14 · arxiv created 2010/07/19 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional TQ equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin-boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these TQ equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from TQ equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is still missing.