Ground-state entanglement in interacting bosonic graphs

¹ Institute for Scientific Interchange (ISI), Villa Gualino Viale Settimio Severo 65, I-10133 Torino, Italy
² Istituto Nazionale per la Fisica della Materia (INFM), UdR Torino-Politecnico I-10129 Torino, Italy
³ Department of Mechanical Engineering, Massachusetts Institute of Technology Cambridge, MA 02139, USA

Received: 24 March 2004
Accepted: 28 June 2004

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 to the rest of the graph (mode entanglement) 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 that leads to the maximum value of the mode entanglement. Whereas in most of the cases one finds the intuitively expected result , we show that 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 crossover between insulating and superfluid ground states.