Reading entanglement in terms of spin configurations in quantum magnets

We consider a quantum many-body system made of $N$ interacting $S{=}1/2$ spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to be in maximally entangled or factorized two-spin states. This result is used in order to capture the meaning of entanglement properties in terms of magnetic behavior. In particular, we consider the concurrence between two spins and show how its expression extracts information on the presence of bipartite entanglement out of the probability distributions relative to specific sets of two-spin quantum states. We apply the above findings to the antiferromagnetic Heisenberg model in a uniform magnetic field, both on a chain and on a two-leg ladder. Using Quantum Monte Carlo simulations, we obtain the above probability distributions and the associated entanglement, discussing their evolution under application of the field.Comment: Final version, to appear in European Physical Journal

Entanglement and factorized ground states in two-dimensional quantum antiferromagnets

Making use of exact results and quantum Monte Carlo data for the entanglement of formation, we show that the ground state of anisotropic two-dimensional S=1/2 antiferromagnets in a uniform field takes the classical-like form of a product state for a particular value and orientation of the field, at which the purely quantum correlations due to entanglement disappear. Analytical expressions for the energy and the form of such states are given, and a novel type of exactly solvable two-dimensional quantum models is therefore singled out. Moreover, we show that the field-induced quantum phase transition present in the models is unambiguously characterized by a cusp minimum in the pairwise-to-global entanglement ratio R, marking the quantum-critical enhancement of \emph{multipartite} entanglement. A detailed discussion is provided on the universality of the cusp in R as a signature of quantum critical behavior entirely based on entanglement.Comment: 4 pages, 3 figure

Staggered magnetization and entanglement enhancement by magnetic impurities in S=1/2S=1/2 spin chain

We study the effects of a magnetic impurity on the behavior of a $S=1/2$ spin chain. At T=0, both with and without an applied uniform magnetic field, an oscillating magnetization appears, whose decay with the distance from the impurity is ruled by a power law. As a consequence, pairwise entanglement is either enhanced or quenched, depending on the distance of the spin pair with respect to the impurity and on the values of the magnetic field and the intensity of the impurity itself. This leads us to suggest that acting on such control parameters, an adiabatic manipulation of the entanglement distribution can be performed. The robustness of our results against temperature is checked, and suggestions about possible experimental applications are put forward.Comment: 4 pages, 8 figure