Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity

TL;DR

This paper explores the geometrical structure of entanglement entropy in relativistic quantum field theories, its relation to gravity, and implications for analogue models of quantum gravity, especially near critical points.

Contribution

It establishes a geometrical framework for entanglement entropy, proposes a conjecture linking entropy density to Newton's constant, and explores implications for quantum gravity in analogue models.

Findings

Entanglement entropy relates to effective gravitational action.

Conjecture: entropy density per area equals 1/(4G_N).

Implications for quantum gravity phenomena and analogue models.

Abstract

A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the subleading terms in the entropy in different dimensions and to behaviour in different states. It is conjectured, on the base of relation between the entropy and the action, that in a fundamental theory the ground state entanglement entropy per unit area equals $1/(4G_N)$, where $G_N$ is the Newton constant in the low-energy gravity sector of the theory. The conjecture opens a new avenue in analogue gravity models. For instance, in higher dimensional condensed matter systems, which near a critical point are described by relativistic QFT's, the entanglement entropy density defines an effective gravitational coupling. By studying the properties of this constant one can get new insights in quantum gravity phenomena, such as the universality of the low-energy physics, the renormalization group behavior of $G_N$, the statistical meaning of the Bekenstein-Hawking entropy.