Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
- 7 February 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 94 (5), 050501
- https://doi.org/10.1103/physrevlett.94.050501
Abstract
We compute the entropy of entanglement between the first 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 as , where and are determined explicitly. In an important class of systems, is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for therefore provides an explicit formula for the central charge.
This publication has 15 references indexed in Scilit:
- Quantum Spin Chain, Toeplitz Determinants and the Fisher–Hartwig ConjectureJournal of Statistical Physics, 2004
- Universality of Entropy Scaling in One Dimensional Gapless ModelsPhysical Review Letters, 2004
- Diverging Entanglement Length in Gapped Quantum Spin SystemsPhysical Review Letters, 2004
- Entanglement and the Phase Transition in Single-Mode SuperradiancePhysical Review Letters, 2004
- Dynamics of entanglement in one-dimensional spin systemsPhysical Review A, 2004
- Entanglement in Quantum Critical PhenomenaPhysical Review Letters, 2003
- Entanglement in a simple quantum phase transitionPhysical Review A, 2002
- Scaling of entanglement close to a quantum phase transitionNature, 2002
- Quantum to classical phase transition in noisy quantum computersPhysical Review A, 2000
- Concentrating partial entanglement by local operationsPhysical Review A, 1996