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

One-particle density matrix of a trapped Lieb\u2013Liniger anyonic gas

We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks\u2013Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids, we provide exact expansions for the one-particle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases