Monogamy of entanglement and improved mean-field ansatz for spin lattices

Abstract

We consider rather general spin-$1/2$ lattices with large coordination numbers $Z$. Based on the monogamy of entanglement and other properties of the concurrence $C$, we derive rigorous bounds for the entanglement between neighboring spins, such as $C\le 1/\sqrt{Z}$, which show that $C$ decreases for large $Z$. In addition, the concurrence $C$ measures the deviation from mean-field behavior and can only vanish if the mean-field ansatz yields an exact ground state of the Hamiltonian. Motivated by these findings, we propose an improved mean-field ansatz by adding entanglement.

arXiv comment4 pages, revtex 4

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Cited by in corpus (6)

• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model
• Large-$d$ phase transitions in holographic mutual information
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Single-layer tensor network approach for three-dimensional quantum systems
• Hierarchy of correlations: Application to Green's functions and interacting topological phases