Scaling of genuine multi particle entanglement close to a quantum phase transition

Quantum phase transitions (QPT), which occur at zero temperature as some physical parameter reaches its critical value, are caused by abrupt changes in the ground state of a many body system. These transitions have been investigated and predicted in many different systems one of which was the one dimensional Ising model in a transverse field. In this work the authors discuss the effects of the QPT on the two-particle entanglement using a finite size scaling ansatz. They also reveal that contrary to the correlation length, which diverges at the QPT, the two particle entanglement stays short ranged. We extend their work from the investigation of two-particle entanglement to genuine multi-particle entanglement in three and four particles reduced states using the computable entanglement monotone for multi particle entanglement arising from the approach of PPT mixtures. Our results show that also multi particle entanglement stays short ranged and follows a scaling behavior as the number of particles in the spin chain is varied.