Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory

Details Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory

2005-04-24

arxiv.org/abs/quant-ph/0504179v1

Phys.Rev.Lett. 94 (2005) 050501

Physics

Quantum Physics

4 pages

Scientific paper

10.1103/PhysRevLett.94.050501

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.

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