Scaling of the R\'enyi entropies in gapped quantum spin systems: Entanglement-driven order beyond symmetry breaking

TL;DR

This paper studies how Rnyi entropies scale in gapped quantum spin chains, revealing entanglement-driven order and oscillatory behaviors that go beyond traditional symmetry-breaking descriptions.

Contribution

It uncovers anomalous Rnyi entropy scaling and introduces a nonlocal order parameter indicating entanglement-driven order beyond symmetry breaking.

Findings

Rnyi b5-entropies with b5 > 2 violate the area law monotonicity

Oscillations in block entropies depend on the factorized ground state

An entanglement-driven order is characterized by a nonlocal order parameter

Abstract

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.