Geometric Entanglement in Valance-Bond-Solid state

Abstract

Multipartite entanglement, measured by the geometric entanglement(GE), is discussed for integer spin Valance-Bond-Solid (VBS) state respectively with periodic boundary condition(PBC) and open boundary condition(OBC) in this paper. The optimization in the definition of geometric entanglement can be reduced greatly by exploring the symmetry of VBS state, and then the fully separable state can be determined explicitly. Numerical evaluation for GE by the random simulation is also implemented in order to demonstrate the validity of the reductions. Our calculations show that GE is saturated by a finite value with the increment of particle number, that means that the total entanglement for VBS state would be divergent under the thermodynamic limit. Moreover it is found that the scaling behavior of GE with spin number $s$ is fitted as $\alpha \log (s+\frac{\beta }{s}+\gamma )+\delta$, in which the values of the parameters $\alpha ,\beta ,\gamma ,\sigma$ are only dependent on the parity of spin $s$. A comparison with entanglement entropy of VBS state is also made, in order to demonstrate the essential differences between multipartite and bipartite entanglement in this model.

This paper has been published by Eur. Phys. J. B 74, 543-553 (2010). However there provides a updated version, in which some expressions and errors are improved and corrected recently for clarity and readablilty.

References in corpus (19)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Entanglement versus Correlations in Spin Systems
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• String order and symmetries in quantum spin lattices
• Multipartite entanglement in spin chains
• Geometric phases and criticality in spin chain systems
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Long-distance entanglement in spin systems
• Multipartite Entanglement Signature of Quantum Phase Transitions
• The geometric measure of entanglement for symmetric states
• Universal geometric entanglement close to quantum phase transitions
• Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
• Exact Analysis of Entanglement in Gapped Quantum Spin Chains
• Entanglement in an SU(n) Valence-Bond-Solid State
• Long-distance entanglement and quantum teleportation in coupled cavity arrays
• Geometric Entanglement in a One-Dimensional Valence Bond Solid State
• Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
• Entanglement and Density Matrix of a Block of Spins in AKLT Model
• Boundary effects to the entanglement entropy and two-site entanglement of the spin-1 valence-bond solid

Cited by in corpus (1)

• Maximal Overlap with a Fully Separable State and Translational Invariance in Multipartite Entangled States