We compute the entropy of entanglement between the first N spins and the rest of the system in the ground states of a general class of quantum spin chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like kappalog(2)N + (κ) over tilde as N --> infinity, where kappa and (κ) over tilde are determined explicitly. In an important class of systems, kappa is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for kappa therefore provides an explicit formula for the central charge.
|Translated title of the contribution||Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory|
|Article number||Art. No. 050501|
|Journal||Physical Review Letters|
|Publication status||Published - 11 Feb 2005|
Bibliographical notePublisher: American Physical Soc
Other identifier: IDS Number: 896NT