@article{OrusLatorreEisertetal.2006,
  author    = {Orus, Roman and Latorre, Jose Ignacio and Eisert, Jens and Cramer, Marcus},
  title     = {Half the entanglement in critical systems is distillable from a single specimen},
  doi       = {10.1103/Physreva.73.060303},
  year      = {2006},
  abstract  = {We establish a quantitative relationship between the entanglement content of a single quantum chain at a critical point and the corresponding entropy of entanglement. We find that, surprisingly, the leading critical scaling of the single-copy entanglement with respect to any bipartitioning is exactly one-half of the entropy of entanglement, in a general setting of conformal field theory and quasifree systems. Conformal symmetry imposes that the single-copy entanglement scales as E-1(rho(L))=(c/6)ln L-(c/6)(pi(2)/ln L)+O(1/L), where L is the number of constituents in a block of an infinite chain and c denotes the central charge. This shows that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to all isotropic quasifree fermionic models. An example of the XY spin chain shows that away from criticality the above relation is maintained only near the quantum phase transition},
  language  = {en}
}
@article{VitaglianoRieraLatorre2010,
  author    = {Vitagliano, Giuseppe and Riera, Arnau and Latorre, Jos{\´e} Ignacio},
  title     = {Volume-law scaling for the entanglement entropy in spin-1/2 chains},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/12/11/113049},
  year      = {2010},
  abstract  = {Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from the locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest-neighbor interactions that presents an entanglement volume scaling law. This non- translational model is contrived to have couplings that force the accumulation of singlet bonds across the half-chain. This configuration of the couplings is suggested by real-space renormalization group arguments. Computation of the entanglement entropy is performed by mapping the system to free fermions and diagonalizing numerically its correlation matrix. An analytical relationship between the entanglement entropy and the Frobenius norm of the correlation matrix is also established. Our result is complementary to the known relationship between non-translational invariant, nearest- neighbor interacting Hamiltonians and quantum Merlin-Arthur (QMA)complete problems.},
  language  = {en}
}