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Entanglement mean field theory: Lipkin–Meshkov–Glick Model

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Abstract

Entanglement mean field theory is an approximate method for dealing with many-body systems, especially for the prediction of the onset of phase transitions. While previous studies have concentrated mainly on applications of the theory on short-range interaction models, we show here that it can be efficiently applied also to systems with long-range interaction Hamiltonians. We consider the (quantum) Lipkin–Meshkov–Glick spin model, and derive the entanglement mean field theory reduced Hamiltonian. A similar recipe can be applied to obtain entanglement mean field theory reduced Hamiltonians corresponding to other long-range interaction systems. We show, in particular, that the zero temperature quantum phase transition present in the Lipkin–Meshkov–Glick model can be accurately predicted by the theory.

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  1. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211 019, India

    Aditi Sen(De) & Ujjwal Sen

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  1. Aditi Sen(De)
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  2. Ujjwal Sen
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Correspondence to Aditi Sen(De).

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Sen(De), A., Sen, U. Entanglement mean field theory: Lipkin–Meshkov–Glick Model. Quantum Inf Process 11, 675–683 (2012). https://doi.org/10.1007/s11128-011-0279-1

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