Violation of area-law scaling for the entanglement entropy in spin 1/2 chains

TL;DR

This paper demonstrates that certain spin 1/2 chains with specific couplings can violate the typical area-law scaling of entanglement entropy, showing volume-law behavior instead, challenging common assumptions about locality.

Contribution

The authors construct a simple, non-translational invariant spin chain Hamiltonian with nearest neighbor interactions that exhibits volume-law entanglement scaling, contrary to usual expectations.

Findings

Constructed a spin chain Hamiltonian with volume-law entanglement

Showed that locality does not necessarily imply area-law scaling

Highlighted the relation to computational complexity classes

Abstract

Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half chain. Our result is complementary to the known relation between non-translational invariant, nearest neighbor interacting Hamiltonians and QMA complete problems.