Integrable spin-boson interaction in the Tavis-Cummings model from a generic boundary twist

Abstract

We construct models describing interaction between a spin $s$ and a single bosonic mode using a quantum inverse scattering procedure. The boundary conditions are generically twisted by generic matrices with both diagonal and off-diagonal entries. The exact solution is obtained by mapping the transfer matrix of the spin-boson system to an auxiliary problem of a spin-$j$ coupled to the spin-$s$ with general twist of the boundary condition. The corresponding auxiliary transfer matrix is diagonalized by a variation of the method of $Q$-matrices of Baxter. The exact solution of our problem is obtained applying certain large-$j$ limit to $su(2{)}_j$, transforming it into the bosonic algebra.

6 pages, revtex; 1 figure. To be published in EPJB

References in corpus (13)

• Quantum Inverse Scattering Method and Correlation Functions
• Chaos and the Quantum Phase Transition in the Dicke Model
• Coherent dynamics of a flux qubit coupled to a harmonic oscillator
• Entanglement and the Phase Transition in Single Mode Superradiance
• Entanglement between two superconducting qubits via interaction with non-classical radiation
• The Los Alamos Trapped Ion Quantum Computer Experiment
• Variational study of the nu=1 quantum Hall ferromagnet in the presence of spin-orbit interaction
• Exact solution for the spin-$s$ XXZ quantum chain with non-diagonal twists
• Steering of a Bosonic Mode with a Double Quantum Dot
• Phase Transitions in Generalised Spin-Boson (Dicke) Models
• Quasi-classical descendants of disordered vertex models with boundaries
• Algebraic approach in unifying quantum integrable models
• Integrable SU(N) vertex models with general toroidal boundary conditions

Cited by in corpus (9)

• Anisotropic Rabi model
• Separation of variables for integrable spin-boson models
• Integrable spin-boson models descending from rational six-vertex models
• Exact quantum dynamics of XXZ central spin problems
• Level statistics of a pseudo-Hermitian Dicke model
• Exact solutions for a family of spin-boson systems
• Quantum Phase Transition in a Pseudo-hermitian Dicke model
• Quantum integrable multi atom matter-radiation models with and without rotating wave approximation
• The Elliptic Gaudin Model: a Numerical Study