Negativity in the Generalized Valence Bond Solid State

Abstract

Using a graphical presentation of the spin $S$ one dimensional Valence Bond Solid (VBS) state, based on the representation theory of the $SU(2)$ 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 non-zero 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 groundstate.

8 pages, 3 Figures. Comments welcomed

References in corpus (8)

• Entanglement negativity in quantum field theory
• Finite temperature entanglement negativity in conformal field theory
• Entanglement negativity in the harmonic chain out of equilibrium
• On the partial transpose of fermionic Gaussian states
• Quantum computational capability of a 2D valence bond solid phase
• String-net model of Turaev-Viro invariants
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Cited by in corpus (3)

• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Entanglement negativity bounds for fermionic Gaussian states
• Entanglement negativity and sudden death in the toric code at finite temperature