Entanglement of Valence-Bond-Solid on an Arbitrary Graph

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dc.creatorXu, Ying
dc.creatorKorepin, Vladimir E
dc.date2008-05-22
dc.date2008-06-01
dc.date.accessioned2026-07-07T10:15:34Z
dc.date.available2026-07-07T10:15:34Z
dc.descriptionThe Affleck-Kennedy-Lieb-Tasaki (AKLT) spin interacting model can be defined on an arbitrary graph. We explain the construction of the AKLT Hamiltonian. Given certain conditions, the ground state is unique and known as the Valence-Bond-Solid (VBS) state. It can be used in measurement-based quantum computation as a resource state instead of the cluster state. We study the VBS ground state on an arbitrary connected graph. The graph is cut into two disconnected parts: the block and the environment. We study the entanglement between these two parts and prove that many eigenvalues of the density matrix of the block are zero. We describe a subspace of eigenvectors of the density matrix corresponding to non-zero eigenvalues. The subspace is the degenerate ground states of some Hamiltonian which we call the block Hamiltonian.
dc.descriptionRevised version, 20 pages, 2 figures; typos corrected, references added
dc.identifierhttps://arxiv.org/abs/0805.3542
dc.identifierhttp://arxiv.org/abs/0805.3542
dc.identifierJ. Phys. A: Math. Theor. 41 505302 (2008)
dc.identifierdoi:10.1088/1751-8113/41/50/505302
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173214
dc.subjectQuantum Physics
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.titleEntanglement of Valence-Bond-Solid on an Arbitrary Graph
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