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Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model

F Leyvraz·WD Heiss
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Abstract

We introduce a novel semiclassical approach to the Lipkin model. In this way the well-known phase transition arising at the critical value of the coupling is intuitively understood. New results -- showing for strong couplings the existence of a threshold energy which separates deformed from undeformed states as well as the divergence of the density of states at the threshold energy -- are explained straightforwardly and in quantitative terms by the appearance of a double well structure in a classical system corresponding to the Lipkin model. Previously unnoticed features of the eigenstates near the threshold energy are also predicted and found to hold.

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F Leyvraz, WD Heiss. 2005-07-01. Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model. https://doi.org/10.1103/physrevlett.95.050402

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