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

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.

4 pages, 2 figures, to appear in PRL

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• Entanglement in a second order quantum phase transition
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• Thermodynamic analogy for quantum phase transitions at zero temperature
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• Quantum phase transitions in the interacting boson model
• Finite-Size Scaling Exponents in the Dicke Model
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• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Quantum quench influenced by an excited-state phase transition
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• Quantum correlations in the collective spin systems
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• Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom
• Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning
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• Virtues and limitations of the truncated Holstein-Primakoff description of quantum rotors
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• Exceptional Points of Resonant States on a Periodic Slab
• Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
• On the Thermodynamic Limit of the Lipkin Model
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• Non-perturbative flow equations from continuous unitary transformations
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