A Spacetime Calculation of the Calabrese-Cardy Entanglement Entropy

TL;DR

This paper computes the spacetime entanglement entropy for a scalar field in 2d cylindrical spacetime, demonstrating universality in the cutoff-dependent term and state-dependent behavior in the size-dependent term.

Contribution

It provides a spacetime calculation of entanglement entropy that confirms the Calabrese-Cardy form and explores the universality and state dependence of its components.

Findings

The cutoff-dependent term is universal with a covariant UV cutoff.

The size-dependent term shows complementarity and depends on the pure state.

The size-dependent coefficient approaches a universal form for certain pure states.

Abstract

We calculate Sorkin's spacetime entanglement entropy of a Gaussian scalar field for complementary regions in the 2d cylinder spacetime and show that it has the Calabrese-Cardy form. We find that the cut-off dependent term is universal when we use a covariant UV cut-off. In addition, we show that the relative size-dependent term exhibits complementarity. Its coefficient is however not universal and depends on the choice of pure state. It asymptotes to the universal form within a natural class of pure states.