Quantum Information Processing

, Volume 15, Issue 11, pp 4581–4598 | Cite as

Negativity in the generalized Valence Bond Solid state

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Abstract

Using a graphical presentation of the spin S one-dimensional Valence Bond Solid (VBS) state, based on the representation theory of the \({\textit{SU}}(2)\) Lie algebra of spins, we compute the spectrum of a mixed-state reduced density matrix. This mixed state of two blocks of spins A and B is obtained by tracing out the spins outside A and B, in the pure VBS state density matrix. We find in particular that the negativity of the mixed state is nonzero only for adjacent subsystems. The method introduced here can be generalized to the computation of entanglement properties in Levin–Wen models, that possess a similar algebraic structure to the VBS state in the ground state.

Keywords

Negativity Entanglement Valence Bond Solid AKLT Lie algebras 

Notes

Acknowledgments

The authors acknowledge the valuable remarks by the anonymous referees, which strengthened this work. R.S. acknowledges F. Duarte and the Physical and Theoretical Chemistry Laboratory at Oxford University, where substantial part of this work was performed. V.K. acknowledges productive atmosphere of Simons Center for Geometry and Physics.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Condensed Matter PhysicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.C.N. Yang Institute for Theoretical PhysicsStony Brook UniversityStony BrookUSA

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