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Tunnelling at finite temperature in the LMG model

Blin, AHHiller, BLi

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

The Lipkin-Meshkov-Glick model is studied at finite temperature in mean The Lipkin-Meshkov-Glick model is studied at finite temperature in mean

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arXiv:0907.3367•Journal of Physics A Mathematical and Theoretical•Oct 22, 2009•14 citations
We investigate the thermal entanglement in the Lipkin—Meshkov—Glick (LMG) model which consists of spin-1/2 particles with XXZ-type exchange interactions between any pair of them. The ferromagnetic (FM) and antiferromagnetic (AFM) cases are completely analyzed at both finite temperature and zero temperature. According to the results obtained by accurate numerical calculation, several interesting physic phenomena and characteristics of thermal entanglement in the LMG model are found. Not only do we evaluate the entanglement of the LMG model, but also discover the correlations between macroscopic physical quantities and thermal entanglement.
The fidelity metric has recently been proposed as a useful and elegant approach to identify and characterize both quantum and classical phase transitions. We study this metric on the manifold of thermal states for the Lipkin–Meshkov–Glick (LMG) model. For the isotropic LMG model, we find that the metric reduces to a Fisher–Rao metric, reflecting an underlying classical probability distribution. Furthermore, this metric can be expressed in terms of derivatives of the free energy, indicating a relation to Ruppeiner geometry. This allows us to obtain exact expressions for the (suitably rescaled) metric in the thermodynamic limit. The phase transition of the isotropic LMG model is signalled by a degeneracy of this (improper) metric in the paramagnetic phase. Due to the integrability of the isotropic LMG model, ground-state level crossings occur, leading to an ill-defined fidelity metric at zero temperature.