Entanglement spectra of superconductivity ground states on the honeycomb lattice

TL;DR

This paper analytically investigates the entanglement spectra of superconducting states in graphene, revealing topological differences between the entanglement Hamiltonian and the subsystem Hamiltonian, especially for chiral d-wave states.

Contribution

It provides an analytical evaluation of entanglement spectra in graphene superconductors, highlighting topological distinctions in entanglement Hamiltonians.

Findings

Entanglement spectra differ topologically from subsystem Hamiltonians.

Chiral d-wave superconductivity shows distinct entanglement properties.

Topological features of entanglement Hamiltonian depend on pairing symmetry.

Abstract

We analytically evaluate the entanglement spectra of the superconductivity states in graphene, primarily focusing on the s-wave and chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity states. We demonstrate that the topology of the entanglement Hamiltonian can differ from that of the subsystem Hamiltonian. In particular, the topological properties of the entanglement Hamiltonian of the chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity state obtained by tracing out one spin direction clearly differ from those of the time-reversal invariant Hamiltonian of noninteracting fermions on the honeycomb lattice.