Entanglement over the rainbow: statistical mechanics of the area law

Entanglement is one of the most salient features of quantum mechanics. In general terms, ground states follow the area law: the entanglement entropy of a block scales like the measure of its boundary.

Yet, engineered ground states in inhomogeneous and random quantum systems may break the area law, and even present maximal entanglement. A relevant example is the 1D rainbow state, which receives its name because symmetrically placed sites with respect to the center of the chain get maximally entangled, and can be understood as the fermionic vacuum on a negatively curved spacetime. In our contribution we will describe the construction of such exotic quantum states which violate the area law, emphasizing the statistical mechanics perspective, e.g. chains with correlated random couplings, and their relation to kinetic roughening and RNA folding [Javier Rodríguez-Laguna et al., 2016 New J. Phys. 18 073025; Vincenzo Alba et al., J. Stat. Mech. (2019) 023105; Nadir Samos Sáenz de Buruaga et al., arXiv:1812.04869].