How robust is the entanglement entropy-area relation?

TL;DR

This paper investigates how the entanglement entropy of a scalar field relates to the area of a sphere, showing that the area law holds for ground, coherent, and squeezed states but is modified for excited states, with implications for black hole entropy.

Contribution

It demonstrates the robustness of the entanglement entropy-area law for certain states and identifies deviations for excited states, providing insights into black hole entropy corrections.

Findings

Area law holds for ground, coherent, and squeezed states.

Excited states lead to entropy scaling as a lower power of the area.

Implications for black hole entropy and quantum gravity theories.

Abstract

We revisit the problem of finding the entanglement entropy of a scalar field on a lattice by tracing over its degrees of freedom inside a sphere. It is known that this entropy satisfies the area law -- entropy proportional to the area of the sphere -- when the field is assumed to be in its ground state. We show that the area law continues to hold when the scalar field degrees of freedom are in generic coherent states and a class of squeezed states. However, when excited states are considered, the entropy scales as a lower power of the area. This suggests that for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power law corrections. We discuss possible implications of this result to black hole entropy.