Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states

Abstract

General local spin $S$ ground states, described by a Valence Bond Solid (VBS) on a two dimensional lattice are studied. The norm of these ground states is mapped to a classical O(3) model on the same lattice. Using this quantum-to-classical mapping we obtain the partial density matrix ${\rho }_A$ associated with a subsystem $A$ of the original ground state. We show that the entanglement spectrum of ${\rho }_{\mathrm{A}}$ in a translation invariant lattice is given by the spectrum of a quantum spin chain at the boundary of region $A$, with local Heisenberg type interactions between spin 1/2 particles.

8 pages, 4 figures, one section and references added

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Cited by in corpus (6)

• Quantum entanglement in condensed matter systems
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Bulk-Edge Correspondence in Fractional Quantum Hall States
• On integrable matrix product operators with bond dimension $D=4$