The Lipkin-Meshkov-Glick model as a particular limit of the \(SU(1,1)\) Richardson-Gaudin integrable models
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Publication:1950565
DOI10.1016/J.NUCLPHYSB.2013.01.019zbMATH Open1262.81261arXiv1212.3238OpenAlexW2073726535MaRDI QIDQ1950565
Author name not available (Why is that?)
Publication date: 13 May 2013
Published in: (Search for Journal in Brave)
Abstract: The Lipkin-Meshkov-Glick (LMG) model has a Schwinger boson realization in terms of a two-level boson pairing Hamiltonian. Through this realization, it has been shown that the LMG model is a particular case of the SU (1, 1) Richardson-Gaudin (RG) integrable models. We exploit the exact solvability of the model tostudy the behavior of the spectral parameters (pairons) that completely determine the wave function in the different phases, and across the phase transitions. Based on the relation between the Richardson equations and the Lam'e differential equations we develop a method to obtain numerically the pairons. The dynamics of pairons in the ground and excited states provides new insights into the first, second and third order phase transitions, as well as into the crossings taking place in the LMG spectrum.
Full work available at URL: https://arxiv.org/abs/1212.3238
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