Entanglement over the rainbow

TL;DR

This paper shows that the rainbow state in an inhomogeneous spin chain acts like a thermofield double of a conformal field theory, revealing connections to black hole physics and extending the model to higher dimensions.

Contribution

It demonstrates that the rainbow state is a thermofield double of a CFT in the weak inhomogeneity limit and proposes higher-dimensional extensions.

Findings

Rainbow state is a thermofield double of a CFT.

Relation between CSP and black holes suggested.

Extension of the model to higher dimensions proposed.

Abstract

In one dimension the area law for the entanglement entropy is violated maximally by the ground state of a strong inhomogeneous spin chain, the so called concentric singlet phase (CSP), that looks like a rainbow connecting the two halves of the chain. In this paper we show that, in the weak inhomogeneity limit, the rainbow state is a thermofield double of a conformal field theory with a temperature proportional to the inhomogeneity parameter. This result suggests some relation of the CSP with black holes. Finally, we propose an extension of the model to higher dimensions.