Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 43, Issue 25, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/43/25/255303
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Funding
- NSF [DMS 0905744]
- MEXT [19340109, 19052004]
- MEXT, Japan
- JSPS [21840021]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [905744] Funding Source: National Science Foundation
- Grants-in-Aid for Scientific Research [19340109, 21840021] Funding Source: KAKEN
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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.
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