# Breaking the Area Law: The Rainbow State

## TL;DR

This paper explores the rainbow phase in 1D critical Hamiltonians where entanglement entropy follows a volume law, revealing connections to conformal field theory, curved spacetime, and quench dynamics.

## Contribution

It introduces the rainbow phase in critical models, links it to thermo-field double states and curved spacetime, and studies its dynamical evolution after quenches.

## Key findings

- Rainbow state exhibits volume law entanglement.
- Rainbow phase can be viewed as a thermo-field double of CFT.
- Rainbow state dynamics studied post-quench.

## Abstract

An exponential deformation of a 1D critical Hamiltonian, with couplings falling on a length scale $h^{-1}$, gives rise to ground states whose entanglement entropy follows a volume law, i.e. the area law is violated maximally. The ground state is now in the so-called {\em rainbow phase}, where valence bonds connect sites on the left half with their symmetric counterparts on the right. Here we discuss some of the most relevant features of this rainbow phase, focusing on the XX and Heisenberg models. Moreover, we show that the rainbow state can be understood either as a thermo-field double of a conformal field theory with a temperature proportional to $h$ or as a massless Dirac fermion in a curved spacetime with constant negative curvature proportional to $h$. Finally, we introduce a study of the time-evolution of the rainbow state after a quench to a homogeneous Hamiltonian.