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

Amico, Luigi; Frahm, Holger; Osterloh, Andreas; Ribeiro, G.A.P.

doi:10.1016/j.nuclphysb.2007.07.022

Cited by 30 publications

(40 citation statements)

References 42 publications

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“…When ǫ = 0, the Hamiltonian enjoys a discrete Z 2 symmetry meaning that the parity of bosonic and spin excitations is conserved. Several attempts of solving these type of models were tried employing Bethe ansatz and Quantum Inverse Scattering techniques [8,9]. The isotropic Rabi model corresponding to θ = 0 and λ = 1 was solved exactly in a seminal paper by Braak [10].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Rabi model

et al. 2014

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We define the anisotropic Rabi model as the generalization of the spin-boson Rabi model: The Hamiltonian system breaks the parity symmetry; the rotating and counterrotating interactions are governed by two different coupling constants; a further parameter introduces a phase factor in the counterrotating terms. The exact energy spectrum and eigenstates of the generalized model are worked out. The solution is obtained as an elaboration of a recently proposed method for the isotropic limit of the model. In this way, we provide a long-sought solution of a cascade of models with immediate relevance in different physical fields, including (i) quantum optics, a two-level atom in single-mode cross-electric and magnetic fields; (ii) solid-state physics, electrons in semiconductors with Rashba and Dresselhaus spin-orbit coupling; and (iii) mesoscopic physics, Josephson-junction flux-qubit quantum circuits.

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Section: Introductionmentioning

confidence: 99%

Anisotropic Rabi model

et al. 2014

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“….., N} are nonzero, which just prove the validity of the induction. Finally, by using the identities: 32) and remarking that A − (λ) has the following functional dependence w.r.t. λ:…”

Section: )mentioning

confidence: 99%

“…In order to study the general representations and boundary conditions we have to go beyond traditional methods which do not apply for these general settings. This is done by developing the Sklyanin's SoV method [84][85][86][87] for this class of models, a method that has the advantage to lead (mainly by construction) to the complete characterization of the spectrum (eigenvalues and eigenvectors) and has proven to be applicable for a large variety of integrable quantum models [28][29][30][31][32][33][34][35][36][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102], where traditional methods fail. Moreover, the SoV approach has the advantage to allow also for the study of the dynamics of the models as it leads to universal determinant formulae for matrix elements of local operators on transfer matrix eigenstates as shown for different classes of models, first in [97], and then in many other cases in [33,88,89,99,100,103].…”

Section: Introductionmentioning

confidence: 99%

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I

2017

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We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the lattice sine-Gordon model with integrable open boundary conditions. This spectral analysis is developed by implementing the method of separation of variables (SoV). The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions. Moreover, we prove an equivalent characterization as the set of solutions to a Baxter's like T-Q functional equation and rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form. In order to explain our method in a simple case, the present paper is restricted to representations containing one constraint on the boundary parameters and on the parameters of the Bazanov-Stroganov Lax operator. In a next article, some more technical tools (like Baxter's gauge transformations) will be introduced to extend our approach to general integrable boundary conditions.

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“…The theory of these equations initiated by Riemann and Fuchs [18] can now be applied to (11). First, one obtains with the definition ψ(z) = φ 1 (z) and ψ(−z) = φ 2 (z) the coupled local system,…”

Section: The Quantum Rabi Modelmentioning

confidence: 99%

Analytical Solutions of Basic Models in Quantum Optics

Braak

2015

Mathematics for Industry

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The recent progress in the analytical solution of models invented to describe theoretically the interaction of matter with light on an atomic scale is reviewed. The methods employ the classical theory of linear differential equations in the complex domain (Fuchsian equations). The linking concept is provided by the Bargmann Hilbert space of analytic functions, which is isomorphic to L 2 (R), the standard Hilbert space for a single continuous degree of freedom in quantum mechanics. I give the solution of the quantum Rabi model in some detail and sketch the solution of its generalization, the asymmetric Dicke model. Characteristic properties of the respective spectra are derived directly from the singularity structure of the corresponding system of differential equations.

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

Cited by 30 publications

References 42 publications

Anisotropic Rabi model

Anisotropic Rabi model

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I

Analytical Solutions of Basic Models in Quantum Optics

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