Daniel D Scherer et al 2009 J. Phys. A: Math. Theor. 42 465304 doi:10.1088/1751-8113/42/46/465304
Finite-temperature fidelity-metric approach to the Lipkin–Meshkov–Glick model
Daniel D Scherer1, Cord A Müller2 and Michael Kastner3
Show affiliationsThe 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.
- PACS
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73.43.Nq Quantum phase transitions
65.40.G- Other thermodynamical quantities
75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.)
- MSC
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74Nxx Phase transformations in solids (See also 74A50, 80Axx, 82B26, 82C26)
- Subjects
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Condensed matter: electrical, magnetic and optical
- Dates
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Issue 46 (20 November 2009)
Received 24 July 2009, in final form 18 September 2009
Published 22 October 2009
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Finite-temperature fidelity-metric approach to the Lipkin–Meshkov–Glick model
Daniel D Scherer et al 2009 J. Phys. A: Math. Theor. 42 465304
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