Extended Lipkin-Meshkov-Glick Hamiltonian

TL;DR

This paper introduces an extended version of the Lipkin-Meshkov-Glick model with a new term that improves the applicability of many-body approximations and better captures the physics of complex systems.

Contribution

The paper proposes a more general Extended LMG Hamiltonian with a new term, enhancing the model's realism and the effectiveness of approximation methods.

Findings

The extended model includes a term depending on the number of particles.

Common many-body approximations better describe the extended model.

The model exhibits symmetry breaking related to system polarization.

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.