Abstract
This note contains discussions on the entanglement entropy and mutual information of a strongly coupled field theory with a critical point which has a holographic dual. We investigate analytically, in the specific regimes of parameters, how these non-local operators behave near the critical point. Interestingly, we observe that although the mutual information is constant at the critical point, its slope shows a power-law divergence in the vicinity of the critical point. We show that the leading behavior of mutual information at and near the critical point could yield a set of critical exponents if we regard it as an order parameter. Our result for this set of static critical exponents is (1/2,1/2,1/2,2) which is identical to the one calculated via the thermodynamic quantities. Hence it suggests that beside the numerous merits of mutual information, this quantity also captures the critical behavior of the underlying field theory and it could be used as a proper measure to probe the phase structure associated with the strongly coupled systems.
Highlights
AND RESULTSFollowing the recent advances in theoretical physics, one could observe that the quantum information theory and quantum gravity have become the frontrunners of current theoretical research programs
We show that the leading behavior of mutual information at and near the critical point could yield a set of critical exponents if we regard it as an order parameter
We based our claim on the result of our analytic calculations for the entanglement entropy and mutual information for the strongly coupled plasma at finite temperature and chemical potential with a critical point using the holographic methods
Summary
Following the recent advances in theoretical physics, one could observe that the quantum information theory and quantum gravity have become the frontrunners of current theoretical research programs. Mutual information would be a more reliable quantity to be used in order to investigate the physical properties of systems described by quantum field theories (QFTs). Since the phase structure of this theory is simple, it provides us with an analytically solvable model to study the behavior of different physical quantities near the critical point. In this paper we use this model to discuss its critical phenomena in terms of information-theoretic measures such as entanglement entropy and mutual information. We obtain these measures analytically, in the context of gauge/gravity duality, within the various thermal limits. We use mutual information, which is a schemeindependent quantity, as an order parameter and discuss its behavior near the critical point. Ð2Þ which are in full agreement with the ones obtained previously in the literature using thermodynamic quantities [41,42,44]
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