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The Lipkin-Meshkov-Glick (LMG) model was devised to test the validity of different approximate formalisms to treat many-particle systems. The model was constructed to be exactly solvable and yet non-trivial, in order to capture some of the main features of real physical systems. In the present contribution, we explicitly review the fact that different many-body approximations commonly used in different fields in physics clearly fail to describe the exact LMG solution. With similar assumptions as those adopted for the LMG model, we propose a new Hamiltonian based on a general two-body interaction. The new model (extended LMG) is not only more general than the original LMG model and, therefore, has a potentially larger spectrum of applicability, but also the physics behind its exact solution can be much better captured by common many-body approximations. At the basis of this improvement lies a new term in the Hamiltonian that depends on the number of constituents and polarizes the system; the associated symmetry breaking is discussed, together with some implications for the study of more realistic systems.

Extended Lipkin-Meshkov-Glick Hamiltonian / R. Romano, X. Roca-Maza, G. Colò, S. Shen. - In: JOURNAL OF PHYSICS. G, NUCLEAR AND PARTICLE PHYSICS. - ISSN 0954-3899. - 48:5(2021 May), pp. 05LT01.1-05LT01.9. [10.1088/1361-6471/abd890]

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