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Abstract: The Affleck-Kennedy-Lieb-Tasaki AKLT spin interacting model can be definedon an arbitrary graph. We explain the construction of the AKLT Hamiltonian.Given certain conditions, the ground state is unique and known as theValence-Bond-Solid VBS state. It can be used in measurement-based quantumcomputation as a resource state instead of the cluster state. We study the VBSground state on an arbitrary connected graph. The graph is cut into twodisconnected parts: the block and the environment. We study the entanglementbetween these two parts and prove that many eigenvalues of the density matrixof the block are zero. We describe a subspace of eigenvectors of the densitymatrix corresponding to non-zero eigenvalues. The subspace is the degenerateground states of some Hamiltonian which we call the block Hamiltonian.

Author: Ying Xu, Vladimir E Korepin

Source: https://arxiv.org/


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