Entanglement vs. gap for one-dimensional spin systems

TL;DR

This paper investigates how entanglement entropy in one-dimensional quantum systems relates to the spectral gap, revealing that some systems exhibit polynomial dependence on 1/Delta, unlike previously known models.

Contribution

The authors construct one-dimensional local systems demonstrating polynomial entanglement entropy dependence on 1/Delta, challenging prior bounds and deepening understanding of entanglement-gap relationships.

Findings

Some systems have entanglement entropy polynomial in 1/Delta

Previous models had entropy bounded by log(1/Delta)

New constructions show larger entropy growth with decreasing gap

Abstract

We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap Delta is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small Delta. To help resolve this asymptotic behavior, we construct a family of one-dimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/Delta, whereas previously studied systems, such as free fermion systems or systems described by conformal field theory, had the entropy of all intervals bounded by a constant times log(1/Delta).