Breaking the Area Law: The Rainbow State

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 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 thermofield 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

Q-deformed rainbows: a universal simulator of free entanglement spectra

“…The ground state of this model is termed the 'concentric singlet phase' [12] or simply 'rainbow state' [13], due to its distinctive structure of maximally entangled valence bonds connecting pairs of sites distributed symmetrically across the center of the chain. This simple model hosts a rich variety of properties [14,15] and has been the subject of much interest in recent years [16][17][18][19].…”