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arXiv · 2009.03593

Extended Lipkin-Meshkov-Glick Hamiltonian

R. Romano·X. Roca-Maza·G. Colò·Shihang Shen
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Abstract

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, with 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.

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R. Romano, X. Roca-Maza, G. Colò, Shihang Shen. 2021-01-06. Extended Lipkin-Meshkov-Glick Hamiltonian. https://doi.org/10.1088/1361-6471%2Fabd890

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