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arXiv · 1509.03215

Entanglement Temperature and Perturbed AdS$_3$ Geometry

G. C. Levine·B. Caravan
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Abstract

In analogy to the first law of thermodynamics, the increase in entanglement entropy $\delta S$ of a conformal field theory (CFT) is proportional to the increase in energy, $\delta E$, of the subsystem divided by an effective entanglement temperature, $T_E$. Extending this analogy, we study entanglement entropy when the subsystem is perturbed by applying an external field, expressed as a coupling to a local marginal operator in the CFT. We show that the resulting entropy change is associated with a change in the entanglement temperature itself, leading to an equation analogous to the Clausius relation. Using AdS/CFT duality we develop a relationship between a perturbation in the local entanglement temperature, $\delta T_E(x)$ of the CFT and the perturbation of the bulk AdS metric. Using the AdS$_3$ minimal surface as a probe, we can construct bulk metric perturbations from an exact numerical computation of the entanglement temperature in a two dimensional $c=1$ boundary theory deformed by a marginal perturbation.

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G. C. Levine, B. Caravan. 2015-09-10. Entanglement Temperature and Perturbed AdS$_3$ Geometry. https://doi.org/10.1103/physrevd.93.126002

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