Entanglement in a Valence-Bond Solid State

Phys. Rev. Lett. 93, 227203 – Published 22 November 2004
Heng Fan, Vladimir Korepin, and Vwani Roychowdhury


We study entanglement in a valence-bond solid state, which describes the ground state of an Affleck-Kennedy-Lieb-Tasaki quantum spin chain, consisting of bulk spin-1's and two spin-1/2's at the ends. We characterize entanglement between various subsystems of the ground state by mostly calculating the entropy of one of the subsystems; when appropriate, we evaluate concurrences as well. We show that the reduced density matrix of a continuous block of bulk spins is independent of the size of the chain and the location of the block relative to the ends. Moreover, we show that the entanglement of the block with the rest of the sites approaches a constant value exponentially fast, as the size of the block increases. We also calculate the entanglement of (i) any two bulk spins with the rest, and (ii) the end spin-1/2's (together and separately) with the rest of the ground state.

DOI: http://dx.doi.org/10.1103/PhysRevLett.93.227203

  • Received 17 June 2004
  • Published 22 November 2004

© 2004 The American Physical Society

Authors & Affiliations

Heng Fan1, Vladimir Korepin2, and Vwani Roychowdhury1

  • 1Electrical Engineering Department, University of California at Los Angeles, Los Angeles, California 90095, USA
  • 2C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3840, USA

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