Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

We study the dynamics of quantum correlations in a class of exactly solvable Ising-type models. We analyze in particular the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. Singletlike states are favored during the propagation, in the sense that tripletlike states change their character during the propagation under certain circumstances. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The “entanglement wave” evolving from a Bell state on the ground state turns out to be very localized in space time. Our findings agree with a recently formulated conjecture on entanglement sharing; some results are interpreted in terms of this conjecture.

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. A mixture of bosonic and/or fermionic atoms can be loaded into the lattice, realizing a generic quantum system of many interacting particles.

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. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this “monogamy” can be lifted for mixed states by virtue of vanishing tangle measures.

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call “comb”. For qubits (or spin $1∕2$) the combs are automatically invariant under $\mathrm{SL}(2,\mathbb{C})$. This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulas for the concurrence and the three-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-qubit entanglement.