Scaling of the R\'enyi entropies in gapped quantum spin systems:   Entanglement-driven order beyond symmetry breaking
  We investigate the scaling of the R\'enyi $\alpha$-entropies in one-dimensional gapped quantum spin models. We show that the block entropies with $\alpha > 2$ violate the area law monotonicity and exhibit damped oscillations. Depending on the existence of a factorized ground state, the oscillatory behavior occurs either below factorization or it extends indefinitely. The anomalous scaling corresponds to an entanglement-driven order that is independent of ground-state degeneracy and is revealed by a nonlocal order parameter defined as the sum of the single-copy entanglement over all blocks. 
S. M. Giampaolo, S. Montangero, F. Dell'Anno, S. De Siena, F.   Illuminati
cond-mat.str-el cond-mat.stat-mech quant-ph