Kitaev chains with long-range pairing

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.