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 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.
Highlights
Entanglement is an effect that has been under a great deal of scrutiny since 1935, when Einstein, Podolsky and Rosen and Schrodinger introduced it as a purely quantum phenomenon without any counterpart in classical physics
The purpose of this paper is to explore a general method of quantifying and bounding total correlations in any such physical system
A great deal of effort has gone into theoretically understanding and quantifying entanglement [2]
Summary
Entanglement is an effect that has been under a great deal of scrutiny since 1935, when Einstein, Podolsky and Rosen and (independently) Schrodinger introduced it as a purely quantum phenomenon without any counterpart in classical physics. The key result of this paper will be a derivation of an upper bound on the amount of total correlation in a thermal state of any macroscopic system. The main advantage of looking at the mutual information as a distance measure, is that it can be generalized in this way to many particles Another advantage is that it can be applied to quantify multipartite entanglement [2] as will be seen later. There is no need to look at the two, three or more subsystems and their entropies Note that this presents an upper bound to total entanglement in the state ρ. We first review how entropies can be used to generalize and formalize the notion of the mean field approximation
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