Entanglement spectra of complex paired superfluids

TL;DR

This paper analyzes the entanglement spectrum of complex paired superfluids in two dimensions, revealing universal edge mode structures and their relation to conformal field theory, with exact solutions for certain pairing functions.

Contribution

It provides explicit solutions for the entanglement spectrum of 2D fermionic superfluids and connects the low-lying spectrum to chiral Majorana modes and conformal field theory.

Findings

Low-lying ES consists of chiral Majorana modes.

Zero-energy modes appear at odd mode numbers.

Entanglement gap diverges near certain pairing functions.

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 BCS form of the ground state wavefunction 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 pseudo-energies of the modes are split in general, but for all l there is a zero--pseudo-energy mode at zero wavevector 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.