On the Thermodynamic Limit of the Lipkin Model

Abstract

The thermodynamic limit of the Lipkin model is investigated. While the limit turns out to be rather elusive, the analysis gives strong indications that the limit yields two analytically dissociated operators, one for the normal and one for the deformed phase. While the Lipkin Hamiltonian is hermitian and has a second order phase transition in finite dimensions (finite particle number), both properties seem to be destroyed in the thermodynamic limit.

9 pages, 3 figures to appear in JPhysA

References in corpus (8)

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• Entanglement in a second order quantum phase transition
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
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Cited by in corpus (9)

• Excited state quantum phase transitions in many-body systems
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Chirality of wave functions for three coalescing levels
• Decoherence as a signature of an excited state quantum phase transition
• Decoherence due to an excited state quantum phase transition in a two-level boson model
• Adiabatic invariants for the regular region of the Dicke model
• Simultaneous fermion and exciton condensations from a model Hamiltonian
• Critical phenomena in light-matter systems with collective matter interactions