Energy space entanglement spectrum of pairing models with s -wave and p -wave symmetry

We study the entanglement between blocks of energy levels in 1D models for s-wave and p-wave superconductivity. The ground state entanglement entropy and entanglement spectrum (ES) of a block of levels around the Fermi point is obtained and related to its physical properties. In the superconducting phase at large coupling, the maximal entropy grows with the number of levels L as 12ln(L). The number of levels presenting maximal entanglement is shown to estimate the number of Cooper pairs involved in pairing correlations. Moreover, the properties of the ES signal the presence of the Read-Green quantum phase transition in the p+ip model, and of the Moore-Read line, which is difficult to characterize. This work establishes a link between physical properties of superconducting phases and quantum entanglement. © 2014 American Physical Society.We thank J. Dukelsky, O. Castro-Alvaredo, and B. Doyon for very useful discussions, and acknowledge financial support from Spanish Government Research Project No. FIS2012-33642 and the Severo Ochoa program. J.R.-L. acknowledges also Research Project No. FIS2009-07277, TOQUATA, and ERC grant QUAGATUA