Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
Keating, J. P. ; Mezzadri, F.
arXiv, 0504179 / Harvested from arXiv
Text on arXiv
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 $\kappa\log_2 N + {\tilde \kappa}$ as $N\to\infty$, where $\kappa$ and ${\tilde \kappa}$ 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.
Publié le : 2005-04-24
Classification:  Quantum Physics,  Mathematical Physics 
@article{0504179,
     author = {Keating, J. P. and Mezzadri, F.},
     title = {Entanglement in Quantum Spin Chains, Symmetry Classes of Random
  Matrices, and Conformal Field Theory},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504179}
}

Keating, J. P.; Mezzadri, F. Entanglement in Quantum Spin Chains, Symmetry Classes of Random
  Matrices, and Conformal Field Theory. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504179/