Entanglement and Density Matrix of a Block of Spins in AKLT Model

Abstract

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1{)}^2$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln (S+1{)}^2$.

Revised version, typos corrected, references added, 31 pages

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• Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian