2007/03/31 by Luigi Amico, L. Amico, H. Frahm +5 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #cond-mat.other #hep-th #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1016/j.nuclphysb.2007.07.022
published as Nucl.Phys.B787:283-300,2007 · 16 pages, 2 eps figures
openalex publication_date 2007/08/01 · arxiv created 2007/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain inhomogeneous rational vertex models combining bosonic and spin representations of SU(2), subject to non-diagonal toroidal and open boundary conditions. Only open boundary conditions are found to lead to integrable Hamiltonians combining both rotating and counter-rotating terms in the interaction. If the boundary matrices can be brought to triangular form simultaneously, the spectrum of the model can be obtained by means of the algebraic Bethe ansatz after a suitable gauge transformation; the corresponding Hamiltonians are found to be non-hermitian. Alternatively, a certain quasi-classical limit of the transfer matrix is considered where hermitian Hamiltonians are obtained as members of a family of commuting operators; their diagonalization, however, remains an unsolved problem.