Entanglement, quantum phase transition, and scaling in the XXZ chain

By S. Gu, Hai-Qing Lin, You-Quan Li. 2003

194 citations recorded by the source corpus.

Motivated by recent development in quantum entanglement, we study relations among concurrence C, ${\mathrm{SU}}_{q}(2)$ algebra, quantum phase transition and correlation length at the zero temperature for the $\mathrm{XXZ}$ chain. We find that at the SU(2) point, the ground state possesses the maximum concurrence. When the anisotropic parameter $\ensuremath{\Delta}$ is deformed, however, its value decreases. Its dependence on $\ensuremath{\Delta}$ scales as ${C=C}_{0}\ensuremath{-}{C}_{1}(\ensuremath{\Delta}\ensuremath{-}{1)}^{2}$ in the $\mathrm{XY}$ metallic phase and near the critical point (i.e., $1l\ensuremath{\Delta}l1.3)$ of the Ising-like insulating phase. We also study the dependence of C on the correlation length $\ensuremath{\xi},$ and show that it satisfies ${C=C}_{0}\ensuremath{-}1/2\ensuremath{\xi}$ near the critical point. For different sizes of the system, we show that there exists a universal scaling function of C with respect to the correlation length $\ensuremath{\xi}.$

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7080a503a91f3ab5e782deefaac52742d078c7d0

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In Artificial Intelligence

  1. Rosario Fazio
  2. Luigi Amico
  3. A. Osterloh
  4. Vlatko Vedral
  5. J. Cardy
  6. Pasquale Calabrese

In Atomic and Molecular Physics, and Optics

  1. Rosario Fazio
  2. Luigi Amico
  3. A. Osterloh
  4. Vlatko Vedral
  5. J. Cardy
  6. Pasquale Calabrese
  7. Michael J. Hartmann

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