Ground-state entanglement in a system with many-body interactions

Entanglement refers to the inability of many-body quantum mechanical systems to be separated into independent subsystems. This has been well investigated in systems consisting of two entangled subsystems. In larger systems, more complex types of entanglement exist. In a system consisting of three subsystems (e. g., qubits), it is possible that all three subsystems are entangled with each other in a way that cannot be reduced to bipartite entanglement, and it is known that two different, inequivalent forms of tripartite entanglement exist such as the GHZ andWstates (GHZ denotes "Greenberger-Horne-Zeilinger"). Here, we investigate a particularly interesting system with competing one-, two-, and three-body interactions. Its ground state can be a product state, a GHZ state, or a W state, depending on the type and strength of the spin-spin couplings. By varying an external control parameter, the system can be made to undergo quantum transitions between the various ground-state-entanglement phases. We implement the system in an NMR quantum simulator and use adiabatic evolution of the effective Hamiltonian to drive the system through the quantum transitions. In the experimental and numerical simulations, we check the suitability of different observables for making the quantum transitions visible and for characterizing the different phases.