%0 Journal Article %J Physical Review Letters %D 2014 %T Kitaev chains with long-range pairing %A Davide Vodola %A Luca Lepori %A Elisa Ercolessi %A Alexey V. Gorshkov %A Guido Pupillo %X We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions. %B Physical Review Letters %V 113 %8 2014/10/9 %G eng %U http://arxiv.org/abs/1405.5440v2 %N 15 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.113.156402