Entanglement in valence-bond-solid states on symmetric graphs

Hosho Katsura, Naoki Kawashima, Anatol N. Kirillov, Vladimir E. Korepin, Shu Tanaka

研究成果: Article査読

22 被引用数 (Scopus)


We study quantum entanglement in the ground state of the Affleck-Kennedy-Lieb-Tasaki model defined on two-dimensional graphs with reflection and/or inversion symmetry. The ground state of this spin model is known as the valence-bond-solid state. We investigate the properties of a reduced density matrix of a subsystem which is a mirror image of the other one. Thanks to reflection symmetry, the eigenvalues of the reduced density matrix can be obtained by numerically diagonalizing a real symmetric matrix whose elements are calculated by Monte Carlo integration. We calculate the von Neumann entropy of the reduced density matrix. The obtained results indicate that there is some deviation from the naive expectation that the von Neumann entropy per valence bond on the boundary between the subsystems is ln 2. This deviation is interpreted in terms of the hidden spin chain along the boundary between the subsystems. In some cases where graphs are on ladders, the numerical results are analytically or algebraically confirmed.

ジャーナルJournal of Physics A: Mathematical and Theoretical
出版ステータスPublished - 2010

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)


「Entanglement in valence-bond-solid states on symmetric graphs」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。