The Dicke model as the contraction limit of a pseudo-deformed Richardson-Gaudin model

Abstract

The Dicke model is derived in the contraction limit of a pseudo-deformation of the quasispin algebra in the su(2)-based Richardson-Gaudin models. Likewise, the integrability of the Dicke model is established by constructing the full set of conserved charges, the form of the Bethe Ansatz state, and the associated Richardson-Gaudin equations. Thanks to the formulation in terms of the pseudo-deformation, the connection from the su(2)-based Richardson-Gaudin model towards the Dicke model can be performed adiabatically.

Exact quantum dynamics of XXZ central spin problems

“…In this context, exact Bethe ansatz solvable models have been particularly fruitful to the study of quantum dynamics of this kind, for example, integrability-based central spin problems [28][29][30][31][32][33][34][35][36][37][38][39], atom-field interacting systems in quantum nonlinear optics [4,40,41], thermalization and quantum dynamics [42][43][44][45], and quantum hydrodynamics [46,47], etc. However, the problem of the size of the Hilbert space increasing exponentially with the particle number still prohibits full analytical accesses to the quantum dynamics at a many-body level.…”

“…A j (s x 0 s x j + s y 0 s y j ) + ∆ j s z 0 s z j , (1) where B is an effective external magnetic field for the central spin [53], N is the number of spins in the bath, A j is the transverse coupling amplitude, and ∆ j is the longitudinal interaction. The model ( 1) is integrable if ∆ j and A j are related through ∆ 2 j −A 2 j = Const., see [32,38,39]. Although this type of models, e.g.…”

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

“…The model is integrable for the coupling constant A k and ∆ k with a constraint. [10][11][12][13][14][15] For the θ = 0 case, the eigenvalues and eigenstates of the Hamiltonian (1) can be exactly solved by the algebraic Bethe ansatz method. [16,17] Based on the exact solutions, on the one hand, an efficient technique has been devised for the numerical solution of the Bethe ansatz equations (BAEs); [18] on the other hand, the thermodynamic limit of the models is a subject of intense research.…”

Separable and entangled states in the high-spin XX central spin model

“…( 3) can be derived from the Gaudin algebra (see, for example, Refs. [9,11,37,38]). Note that there also exists a class of spin-1/2 XXZ integrable models built from non-skew symmetric r-matrices, which do not necessarily obey Eq.…”