Scaling of genuine multiparticle entanglement close to a quantum phase transition

Abstract

We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional $XY$ model at the quantum phase transition. We observe a logarithmic divergence, show that genuine three- and four-particle entanglement obeys finite-size scaling of the $XY$ model and demonstrate that the genuine three-particle entanglement has a finite spatial range.