In this talk I will first introduce classical and quantum long-range Ising models and their field theory counterparts. I will show that in particular regimes these systems can be described with simple free non-local field theories with dispersion relation $\omega(k)=|k|^{\alpha/2}$. Having this motivation in mind I will first study many quantum aspects of free non-local field theories such as: the entanglement entropy, dynamics of local operators and entanglement entropy after quantum quenches. Then in particular cases I will also  present some results  regarding interacting field theories.

 

1: M. A. Rajabpour, S. Sotiriadis, Phys. Rev. B 91, 045131 (2015)

2: M. Ghasemi Nezhadhaghighi, M. A. Rajabpour,  EPL, 100 (2012) 60011 and Phys. Rev. B 88, 045426 (2013) and  Phys. Rev. B 90, 205438 (2014)