Block spin density matrix of the inhomogeneous AKLT model

  • Authors:

  • Ying Xu;Hosho Katsura;Takaaki Hirano;Vladimir E. Korepin

  • Affiliations:

  • C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, USA 11794-3840;Department of Applied Physics, The University of Tokyo, Tokyo, Japan 113-8656;Department of Applied Physics, The University of Tokyo, Tokyo, Japan 113-8656;C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, USA 11794-3840

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2008

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Abstract

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.