More on the rainbow chain: entanglement, space-time geometry and thermal states

TL;DR

This paper reveals that the rainbow chain's universal properties are described by a massless Dirac fermion in curved space-time, enabling analytical entanglement entropy calculations and exploring thermal state behaviors.

Contribution

It identifies the quantum field theory underlying the rainbow chain as a massless Dirac fermion in curved space-time, advancing understanding of its entanglement properties.

Findings

Entanglement entropy scales with system size in the ground state.

Analytical characterization of bipartition entanglement entropies.

Non-trivial interplay between rainbow effective temperature and physical temperature.

Abstract

The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature $R=-h^2$ ($h$ is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature $T_R$ and the physical temperature $T$.