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≤1/Z, which show that C decreases for large Z. In addition, we demonstrate that 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.