Ground-State Entanglement in Interacting Bosonic Graphs

Abstract

We consider a collection of bosonic modes corresponding to the vertices of a graph $Γ.$ Quantum tunneling can occur only along the edges of $Γ$ and a local self-interaction term is present. Quantum entanglement of one vertex with respect the rest of the graph is analyzed in the ground-state of the system as a function of the tunneling amplitude $τ.$ The topology of $Γ$ plays a major role in determining the tunneling amplitude $τ^*$ which leads to the maximum ground-state entanglement. Whereas in most of the cases one finds the intuitively expected result $τ^*=\infty$ we show that it there exists a family of graphs for which the optimal value of$τ$ is pushed down to a finite value. We also show that, for complete graphs, our bi-partite entanglement provides useful insights in the analysis of the cross-over between insulating and superfluid ground states