Integrable spin-boson models descending from rational six-vertex models

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.

16 pages, 2 eps figures

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Cited by in corpus (19)

• On the Integrability of the Rabi Model
• Anisotropic Rabi model
• Integrability vs exact solvability in the quantum Rabi and Dicke models
• Entanglement dynamics of two independent Jaynes-Cummings atoms without rotating-wave approximation
• Separation of variables for integrable spin-boson models
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Solution of the Dicke model for N=3
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Exact solutions for a family of spin-boson systems
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Beyond adiabatic elimination: Effective Hamiltonians and singular perturbation
• Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits
• Analytical solutions of basic models in quantum optics
• On Separation of Variables for Reflection Algebras
• Application of polaron picture in the two-qubit quantum Rabi model
• Quasi-Exactly Solvable Models Derived from the Quasi-Gaudin Algebra