Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence

Details Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence

2011-07-20

arxiv.org/abs/1107.3888v4

Phys. Rev. B 84, 245128 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

10 pages, 9 figures, published version

Scientific paper

10.1103/PhysRevB.84.245128

We investigate the entanglement properties of the valence-bond-solid (VBS) state defined on two-dimensional lattices, which is the exact ground state of the Affleck-Kennedy-Lieb-Tasaki model. It is shown that the entanglement entropy obeys an area law and the non-universal prefactor of the leading term is strictly less than $\ln 2$. The analysis of entanglement spectra for various lattices reveals that the reduced density matrix associated with the VBS state is closely related to a thermal density matrix of a {\it holographic} spin chain, whose spectrum is reminiscent of that of the spin-1/2 Heisenberg chain. This correspondence is further supported by comparing the entanglement entropy in the holographic spin chain with conformal field theory predictions.

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