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Ground-State Entanglement in Interacting Bosonic Graphs

Paolo Giorda·Paolo Zanardi
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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

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Paolo Giorda, Paolo Zanardi. 2003-11-10. Ground-State Entanglement in Interacting Bosonic Graphs. https://doi.org/10.1209/epl%2Fi2004-10129-2

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