Mutual information between thermo-field doubles and disconnected holographic boundaries

TL;DR

This paper investigates the entanglement between physical and thermo-field double degrees of freedom at finite temperature using mutual information, analyzing simple models and holographic systems to reveal key properties and their theoretical implications.

Contribution

It introduces the concept of thermo-mutual information in finite-temperature field theories and explores its properties in toy models and holographic duals, connecting it to minimal surfaces and the Schwinger-Keldysh formalism.

Findings

Thermo-mutual information is UV finite and positive.

It is bounded above by the standard mutual information.

Connections to minimal surfaces in holography are established.

Abstract

We use mutual information as a measure of the entanglement between 'physical' and thermo-field double degrees of freedom in field theories at finite temperature. We compute this "thermo-mutual information" in simple toy models: a quantum mechanics two-site spin chain, a two dimensional massless fermion, and a two dimensional holographic system. In holographic systems, the thermo-mutual information is related to minimal surfaces connecting the two disconnected boundaries of an eternal black hole. We derive a number of salient features of this thermo-mutual information, including that it is UV finite, positive definite and bounded from above by the standard mutual information for the thermal ensemble. We relate the construction of the reduced density matrices used to define the thermo-mutual information to the Schwinger-Keldysh formalism, ensuring that all our objects are well defined in Euclidean and Lorentzian signature.