Integrable spin-boson models descending from rational six-vertex models
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Publication:2461654
DOI10.1016/J.NUCLPHYSB.2007.07.022zbMATH Open1225.82018arXivcond-mat/0703630OpenAlexW2020644716WikidataQ62582601 ScholiaQ62582601MaRDI QIDQ2461654
Author name not available (Why is that?)
Publication date: 21 November 2007
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/cond-mat/0703630
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