Entanglement in valence-bond-solid states on symmetric graphs

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

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number255303
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number25
DOIs
Publication statusPublished - 2010
Externally publishedYes

Fingerprint

Symmetric Graph
Density Matrix
Entanglement
Subsystem
solid state
valence
Ground State
Deviation
Entropy
entropy
Ground state
deviation
Monte Carlo Integration
Reflectional symmetry
Quantum Entanglement
ground state
Spin Chains
Quantum entanglement
Spin Models
symmetry

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Entanglement in valence-bond-solid states on symmetric graphs. / Katsura, Hosho; Kawashima, Naoki; Kirillov, Anatol N.; Korepin, Vladimir E.; Tanaka, Shu.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 25, 255303, 2010.

Research output: Contribution to journalArticle

Katsura, Hosho ; Kawashima, Naoki ; Kirillov, Anatol N. ; Korepin, Vladimir E. ; Tanaka, Shu. / Entanglement in valence-bond-solid states on symmetric graphs. In: Journal of Physics A: Mathematical and Theoretical. 2010 ; Vol. 43, No. 25.
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