Related papers: Analytical Solutions to Asymmetric Two-Photon Rabi…
We study the highest weight representations of the RTT algebras for the R matrix of sp_q(2n) type by the nested algebraic Bethe ansatz. It is a generalization of our study for R matrix of sp(2n) and so(2n) type
Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…
We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of…
A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It…
The aim of this paper is a better understanding for the eigenstates of the asymmetric quantum Rabi model by Lie algebra representations of $\mathfrak{sl}_2$. We define a second order element of the universal enveloping algebra…
We consider a generalization of the quantum Rabi model where the two-level system and the single-mode cavity oscillator are coupled by an additional Stark-like term. By adapting a method recently introduced by Braak [Phys. Rev. Lett. {\bf…
A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic…
We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of…
Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the…
We study a cavity-QED setup consisting of a two-level system coupled to a single cavity mode with two-photon relaxation. The system dynamics is modeled via a Lindblad master equation consisting of the Rabi Hamiltonian and a two-photon…
We present an analytical method for the two-qubit quantum Rabi model. While still operating in the frame of the generalized rotating-wave approximation (GRWA), our method further embraces the idea of introducing variational parameters. The…
We consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third order differential equations with…
The generalized Rabi model (gRM) with both one- and two-photon coupling terms has been successfully implemented in circuit quantum electrodynamics systems. In this paper, we examine theoretically multiphoton resonances in the gRM and derive…
We study solutions of the Bethe ansatz equation for the XXZ-type integrable model associated with the Lie algebra sl_N. We give a correspondence between solutions of the Bethe ansatz equations and collections of quasi-polynomials. This…
We revisit the Jaynes-Cummings and anti-Jaynes-Cummings model through the lens of Lie theory, aiming to highlight the efficacy of an operator-based approach for diagonalization. We focus on explicitly delineating the steps from an…
We propose a set of photonic crystals that realize a nonlinear quantum Rabi model equivalent to a two-level system driven by the phase of a quantized electromagnetic field. The crystals are exactly soluble in the weak-coupling regime and…
In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we…
We derive a number of results related to the Gaudin model associated to the simple Lie algebra of type G$_2$. We compute explicit formulas for solutions of the Bethe ansatz equations associated to the tensor product of an arbitrary…
We apply the method of differential renormalization to two and three dimensional abelian gauge theories. The method is especially well suited for these theories as the problems of defining the antisymmetric tensor are avoided and the…