Mean-field approximations and multipartite thermal correlations
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 find an upper bound for the total amount of correlations (and hence entanglement) in a phy...
| Main Author: | |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
IOP Publishing
2004
|
| _version_ | 1826264085929394176 |
|---|---|
| author | Vedral, V |
| author_facet | Vedral, V |
| author_sort | Vedral, V |
| collection | OXFORD |
| description | 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 find an upper bound for 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 by using two qubits interacting through the Heisenberg coupling, where entanglement and correlations can be computed exactly. It is then applied to the one-dimensional (1D) Ising model in a transverse magnetic field, for which entanglement and correlations cannot be obtained by exact methods. We analyse the behaviour 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 correspond to a (d + 1)-dimensional classical system in equilibrium to substitute all entanglement for classical correlations. |
| first_indexed | 2024-03-06T20:02:07Z |
| format | Journal article |
| id | oxford-uuid:27aa6c01-a464-480a-a1e5-36bb4b9bdea4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:02:07Z |
| publishDate | 2004 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:27aa6c01-a464-480a-a1e5-36bb4b9bdea42022-03-26T12:08:15ZMean-field approximations and multipartite thermal correlationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:27aa6c01-a464-480a-a1e5-36bb4b9bdea4EnglishSymplectic Elements at OxfordIOP Publishing2004Vedral, VThe 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 find an upper bound for 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 by using two qubits interacting through the Heisenberg coupling, where entanglement and correlations can be computed exactly. It is then applied to the one-dimensional (1D) Ising model in a transverse magnetic field, for which entanglement and correlations cannot be obtained by exact methods. We analyse the behaviour 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 correspond to a (d + 1)-dimensional classical system in equilibrium to substitute all entanglement for classical correlations. |
| spellingShingle | Vedral, V Mean-field approximations and multipartite thermal correlations |
| title | Mean-field approximations and multipartite thermal correlations |
| title_full | Mean-field approximations and multipartite thermal correlations |
| title_fullStr | Mean-field approximations and multipartite thermal correlations |
| title_full_unstemmed | Mean-field approximations and multipartite thermal correlations |
| title_short | Mean-field approximations and multipartite thermal correlations |
| title_sort | mean field approximations and multipartite thermal correlations |
| work_keys_str_mv | AT vedralv meanfieldapproximationsandmultipartitethermalcorrelations |