Entanglement between particle partitions in itinerant many-particle states

We review `particle partitioning entanglement' for itinerant many-particle systems. This is defined as the entanglement between two subsets of particles making up the system. We identify generic features and mechanisms of particle entanglement that are valid over whole classes of itinerant quantum systems. We formulate the general structure of particle entanglement in many-fermion ground states, analogous to the `area law' for the more usually studied entanglement between spatial regions. Basic properties of particle entanglement are first elucidated by considering relatively simple itinerant models. We then review particle-partitioning entanglement in quantum states with more intricate physics, such as anyonic models and quantum Hall states.Comment: review, about 20 pages. Version 2 has minor revisions

Entanglement properties and moment distributions of a system of hard-core anyons on a ring

We study the one-particle von Neumann entropy of a system of N hard-core anyons on a ring. The entropy is found to have a clear dependence on the anyonic parameter which characterizes the generalized fractional statistics described by the anyons. This confirms the entanglement as a valuable measure to investigate topological properties of quantum states. Furthermore, we determine analytically the large N asymptotics of the anyonic one-particle density matrix. The formula presented here generalizes the Lenard formula obtained for a system of N hard-core bosons. Finally, we present a numerical analysis which confirms the analytical results and provides additional insight into the problem under consideration.Comment: 5 pages, 3 eps figures. v2: Fig 3 changed, Eq 13 changed, minor corrections. References adde

A short review on entanglement in quantum spin systems

We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.Comment: 20 pages and 6 figures. Review article for the special issue "Entanglement entropy in extended systems" in J. Phys. A, edited by P. Calabrese, J. Cardy and B. Doyo