Avalanche of entanglement and correlations at quantum phase transitions.

We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling J and find a sequential increase of entanglement depth d with growing J. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for J = ∞, arriving at a pure L-partite (GHZ type) entanglement of all L spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small J.

Entangled three-qubit states without concurrence and three-tangle.

We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle.

Enhancement of pairwise entanglement via Z2 symmetry breaking.

We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition.

Quantum many particle systems in ring-shaped optical lattices.

In the present work we demonstrate how to realize a 1D closed optical lattice experimentally, including a tunable boundary phase twist. The latter may induce "persistent currents" visible by studying the atoms' momentum distribution. We show how important phenomena in 1D physics can be studied by physical realization of systems of trapped atoms in ring-shaped optical lattices.

Exact correlation functions of the BCS model in the canonical ensemble.

We evaluate correlation functions of the BCS model for a finite number of particles. The integrability of the Hamiltonian relates it with the Gaudin algebra G[sl(2)]. Therefore, a theorem that Sklyanin proved for the Gaudin model, can be applied.