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

Luigi Amico A, Holger Frahm, Andreas Osterloh +1 more

arXiv:cond-mat/0703630Nuclear Physics BAug 1, 200757 citations

Separation of variables in the quantum integrable models related to the Yangiany[sl(3)]

E. K. Sklyanin

arXiv:hep-th/9212076Journal of Mathematical SciencesJun 1, 199677 citations

Characterization of Quantum and Classical Critical Points for an Integrable Two-Qubit Spin–Boson Model

Roberto Grimaudo, ANTONINO MESSINA, Hiromichi Nakazato +2 more

The class of two-interacting-qubit spin–boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin–boson models where the role of the tunneling parameter is played by the spin–spin coupling. The dynamics of the magnetization are analyzed for different levels of (an)isotropy. The existence of a decoherence-free subspace, as well as of different classical regimes separated by a critical temperature, and symptoms of quantum (first-order and Kosterlitz–Thouless type) phase transitions in the Ohmic regime are brought to light.The class of two-interacting-qubit spin–boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin–boson models where the role of the tunneling parameter is played by the spin–spin coupling. The dynamics of the magnetization are analyzed for different levels of (an)isotropy. The existence of a decoherence-free subspace, as well as of different classical regimes separated by a critical temperature, and symptoms of quantum (first-order and Kosterlitz–Thouless type) phase transitions in the Ohmic regime are brought to light.

SymmetryDec 7, 20232 citations

Integrable central spin models

Jaco van Tonder

Nov 14, 20250 citations

Dynamics of the spin–boson system

Ulrich Weiß, Maura Sassetti

WORLD SCIENTIFIC eBooksDec 1, 19933 citations

Separation of variables for higher rank integrable models: review of recent progress

Fedor Levkovich-Maslyuk

Abstract Separation of variables (SoVs) is a powerful method expected to be applicable for a wide range of quantum integrable systems, from models in condensed matter physics to gauge and string theories. Yet its full implementation for many higher rank examples, such as SU(N) spin chains with N > 2, has remained elusive for a long time. In this pedagogical review we discuss the major progress achieved recently in understanding SoV for models of this type. In particular, for rational SU(N) spin chains we describe different constructions of the SoV basis, novel compact forms for spin chain eigenstates, the functional SoV approach, and explicit computation of the SoV measure. We also discuss key first applications of these results, namely the new compact determinant representations for many observables such as scalar products and correlators.Abstract Separation of variables (SoVs) is a powerful method expected to be applicable for a wide range of quantum integrable systems, from models in condensed matter physics to gauge and string theories. Yet its full implementation for many higher rank examples, such as SU(N) spin chains with N > 2, has remained elusive for a long time. In this pedagogical review we discuss the major progress achieved recently in understanding SoV for models of this type. In particular, for rational SU(N) spin chains we describe different constructions of the SoV basis, novel compact forms for spin chain eigenstates, the functional SoV approach, and explicit computation of the SoV measure. We also discuss key first applications of these results, namely the new compact determinant representations for many observables such as scalar products and correlators.

arXiv:2503.15398Journal of Physics A Mathematical and TheoreticalJun 4, 20253 citations

Separation of variables for integrable spin–boson models

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