dorsal/arxiv
View SchemaMean Field Approximations and Multipartite Thermal Correlations
| Authors | Vlatko Vedral |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312104 |
| URL | https://arxiv.org/abs/quant-ph/0312104 |
| DOI | 10.1088/1367-2630/6/1/022 |
| Journal | New J. Phys. 6: art. no. 22 Feb. 10 (2004) |
Abstract
The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to bound the total amount of correlations (and hence entanglement) in a physical system in thermal equilibrium at some temperature in terms of its free energy and internal energy. This method is first illustrated using two qubits interacting through the Heisenberg coupling, where entanglement and correlations can be computed exactly. It is then applied to the one dimensional Ising model in a transverse magnetic field, for which entanglement and correlations cannot be obtained by exact methods. We analyze the behavior of correlations in various regimes and identify critical regions, comparing them with already known results. Finally, we present a general discussion of the effects of entanglement on the macroscopic, thermodynamical features of solid-state systems. In particular, we exploit the fact that a $d$ dimensional quantum system in thermal equilibrium can be made to corresponds to a d+1 classical system in equilibrium to substitute all entanglement for classical correlations.
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"abstract": "The relationship between the mean-field approximations in various interacting\nmodels of statistical physics and measures of classical and quantum\ncorrelations is explored. We present a method that allows us to bound the total\namount of correlations (and hence entanglement) in a physical system in thermal\nequilibrium at some temperature in terms of its free energy and internal\nenergy. This method is first illustrated using two qubits interacting through\nthe Heisenberg coupling, where entanglement and correlations can be computed\nexactly. It is then applied to the one dimensional Ising model in a transverse\nmagnetic field, for which entanglement and correlations cannot be obtained by\nexact methods. We analyze the behavior of correlations in various regimes and\nidentify critical regions, comparing them with already known results. Finally,\nwe present a general discussion of the effects of entanglement on the\nmacroscopic, thermodynamical features of solid-state systems. In particular, we\nexploit the fact that a $d$ dimensional quantum system in thermal equilibrium\ncan be made to corresponds to a d+1 classical system in equilibrium to\nsubstitute all entanglement for classical correlations.",
"arxiv_id": "quant-ph/0312104",
"authors": [
"Vlatko Vedral"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/6/1/022",
"journal_ref": "New J. Phys. 6: art. no. 22 Feb. 10 (2004)",
"title": "Mean Field Approximations and Multipartite Thermal Correlations",
"url": "https://arxiv.org/abs/quant-ph/0312104"
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