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J. Phys. Soc. Jpn. 76 (2007) 074603 (4 pages)  |Previous Article| |Next Article|  |Table of Contents|
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Entanglement Entropy of One-dimensional Gapped Spin Chains

Takaaki Hirano1 and Yasuhiro Hatsugai1,2

1Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656
2Institute of Physics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571

(Received March 19, 2007; Accepted May 8, 2007; Published July 10, 2007)

We investigate the entanglement entropy (EE) of gapped S=1 and S=1/2 spin chains with dimerization. We find that the effective boundary degrees of freedom as edge states contribute significantly to the EE. For the S=1/2 dimerized Heisenberg chain, the EE of the sufficiently long chain is essentially explained by the localized S=1/2 effective spins on the boundaries. As for S=1, the effective spins are also S=1/2 causing a Kennedy triplet that yields a lower bound for the EE. In this case, the residual entanglement reduces substantially by a continuous deformation of the Heisenberg model to that of the AKLT Hamiltonian. ©2007 The Physical Society of Japan

KEYWORDS: topological orders, quantum phase transition, entanglement entropy, spin chains, Haldane gap, edge states
URL: http://jpsj.ipap.jp/link?JPSJ/76/074603/
DOI: 10.1143/JPSJ.76.074603


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