We consider entanglement properties of pure finitely correlated states (FCS). We derive bounds for the entanglement of a spin with an interval of spins in an arbitrary pure FCS. Finitely correlated states are also known as matrix product states or generalized valence-bond states. The bounds become exact in the case where one considers the entanglement of a single spin with a half-infinite chain to the right of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for nonvanishing entanglement in terms of a single spin and the memory of the FCS is also sufficient. We also generalize the study of entanglement in the Affleck-Kennedy-Lieb-Tasaki model by Fan, Korepin, and Roychowdhury. Our result permits a more efficient calculation, numerically and in some cases analytically, of the entanglement of arbitrary finitely correlated quantum spin chains.We consider entanglement properties of pure finitely correlated states (FCS). We derive bounds for the entanglement of a spin with an interval of spins in an arbitrary pure FCS. Finitely correlated states are also known as matrix product states or generalized valence-bond states. The bounds become exact in the case where one considers the entanglement of a single spin with a half-infinite chain to the right of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for nonvanishing entanglement in terms of a single spin and the memory of the FCS is also sufficient. We also generalize the study of entanglement in the Affleck-Kennedy-Lieb-Tasaki model by Fan, Korepin, and Roychowdhury. Our result permits a more efficient calculation, numerically and in some cases analytically, of the entanglement of arbitrary finitely correlated quantum spin chains.

arXiv:math-ph/0606018Physical Review LettersOct 4, 200611 citations

APPLICATIONS OF FINITELY CORRELATED STATES TO THE GROUND STATE PROBLEM OF QUANTUM SPIN CHAINS

Bruno Nachtergaele

QP-PQ, quantum probability and white noise analysisJul 1, 19920 citations

Correlated States of Quantum Chain

Olga V. Man’ko

Springer eBooksApr 7, 20080 citations

Entangled finitely correlated quantum spin chains

Fabio Benatti, Beatrix C. Hiesmayr, Heide Narnhofer

We study the multipartite entanglement properties of translation-invariant states of infinite quantum spin chains with a valence-bond structure.

Laser PhysicsApr 1, 20060 citations

Large Deviations in Quantum Spin Chain

Yoshiko Ogata

We show the full large deviation principle for KMS-states and $C^*$ -finitely correlated states on a quantum spin chain. We cover general local observables. Our main tool is Ruelle's transfer operator method.We show the full large deviation principle for KMS-states and $C^*$-finitely correlated states on a quantum spin chain. We cover general local observables. Our main tool is Ruelle's transfer operator method.

arXiv:0803.0113Mar 2, 20086 citations

We show the full large deviation principle for KMS-states and

C^*

-finitely correlated states on a quantum spin chain. We cover general local observables. Our main tool is Ruelle's transfer operator method.