Entanglement spectra of superconductivity ground states on the honeycomb lattice

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.