A refinement of entanglement entropy and the number of degrees of freedom

TL;DR

This paper introduces a UV-finite 'renormalized entanglement entropy' that tracks the degrees of freedom at different scales, providing insights into RG flow and conformal properties across various quantum field theories.

Contribution

It proposes a new scale-dependent entanglement measure that interpolates between UV and IR fixed points and explores its properties in different dimensions.

Findings

Reduces to the central charge in conformal theories

Interpolates between UV and IR fixed points

Potential non-monotonicity in four dimensions

Abstract

We introduce a "renormalized entanglement entropy" which is intrinsically UV finite and is most sensitive to the degrees of freedom at the scale of the size R of the entangled region. We illustrated the power of this construction by showing that the qualitative behavior of the entanglement entropy for a non-Fermi liquid can be obtained by simple dimensional analysis. We argue that the functional dependence of the "renormalized entanglement entropy" on R can be interpreted as describing the renormalization group flow of the entanglement entropy with distance scale. The corresponding quantity for a spherical region in the vacuum, has some particularly interesting properties. For a conformal field theory, it reduces to the previously proposed central charge in all dimensions, and for a general quantum field theory, it interpolates between the central charges of the UV and IR fixed points as R is varied from zero to infinity. We conjecture that in three (spacetime) dimensions, it is always non-negative and monotonic, and provides a measure of the number of degrees of freedom of a system at scale R. In four dimensions, however, we find examples in which it is neither monotonic nor non-negative.