Diverging Entanglement Length in Gapped Quantum Spin Systems

We prove the existence of gapped quantum Hamiltonians whose ground states exhibit an infinite entanglement length, as opposed to their finite correlation length. Using the concept of entanglement swapping, the localizable entanglement is calculated exactly for valence bond and finitely correlated states, and the existence of the so-called string-order parameter is discussed. We also report on evidence that the ground state of an antiferromagnetic chain can be used as a perfect quantum channel if local measurements on the individual spins can be implemented.

Figure 1

(a) The valence bond ground state of the AKLT model (1); each edge represents a singlet, and the dashed circle corresponds to a projection onto the symmetric subspace. (b) A deformed AKLT model where the singlets are replaced by nonmaximally entangled states $|\varphi ⟩$.

Figure 2

Correlation length ${\xi }_C$ (solid) and of the entanglement length ${\xi }_E$ (dotted) for the ground state of the deformed AKLT Hamiltonians $H(\varphi )$ (7).