Entanglement spectra of complex paired superfluids.

ABSTRACT

We study the entanglement in various fully gapped complex paired states of fermions in two dimensions, focusing on the entanglement spectrum (ES), and using the Bardeen-Cooper-Schrieffer (BCS) form of the ground-state wave function on a cylinder. Certain forms of the pairing functions allow a simple and explicit exact solution for the ES. In the weak-pairing phase of ℓ-wave paired spinless fermions (ℓ odd), the universal low-lying part of the ES consists of |ℓ| chiral Majorana fermion modes [or 2|ℓ| (ℓ even) for spin-singlet states]. For |ℓ|>1, the pseudoenergies of the modes are split in general, but for all ℓ there is a zero-pseudoenergy mode at a zero wave vector if the number of modes is odd. This ES agrees with the perturbed conformal field theory of the edge excitations. For more general BCS states, we show how the entanglement gap diverges as a model pairing function is approached.