Negativity in the generalized Valence Bond Solid state

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• 作者：Raul A. Santos ; V. Korepin
• 关键词：Negativity ; Entanglement ; Valence Bond Solid ; AKLT ; Lie algebras
• 刊名：Quantum Information Processing
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：15
• 期：11
• 页码：4581-4598
• 全文大小：1,292 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332
• 卷排序：15

文摘

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.