Boundedness of Entanglement Entropy,and Split Property of Quantum Spin Chains

TL;DR

This paper establishes that bounded entanglement entropy in quantum spin chains implies the split property of subsystems, with implications for ground states and gapless excitations in certain models.

Contribution

It proves the link between entanglement entropy boundedness and the split property, and applies this to infinite volume ground states and gapless excitations in quantum spin chains.

Findings

Bounded entanglement entropy implies split property.

Infinite volume ground states with spectral gap have split property.

Gapless excitations occur under certain conditions in spinless Fermion models.

Abstract

We show the boundedness of entanglement entropy for (bipartite) pure states of quantum spin chains implies split property of subsystems. As a corollary the infinite volume ground states for 1-dim spin chains with the spectral gap between the ground state energy and the rest of spectrum have the split property. We see gapless excitation exists for the spinless Fermion on $\bfZ$ if the ground state is non-trivial and translationally invariant and the U(1) gauge symmetry is unbroken. Here we do not assume uniqueness of ground states for all finite volume Hamiltonians.