Bosonic Dirac Materials on a honeycomb antiferromagnetic Ising model

Motivated by the recent proposal of Bosonic Dirac materials (BDM), we revisited the Ising model on a honeycomb lattice in the presence of the longitudinal and transverse fields. We apply linear spin-wave theory to obtain the magnon dispersion and its degenerated points. These special degenerated points emerge on the excitation spectrum as a function of the external fields and can be identified as Bosonic Dirac Points (BDP). Since that, in the vicinity of these points the Magnons becomes massless with a linear energy spectrum as well as insensible in relation to weak impurity, exactly as it occurs with a Fermionic Dirac point. We also have calculated the quantum and thermal fluctuations over the ground state of the system using Effective Field Theory. Our results point out that this simple model can host Bosonic Dirac points and therefore is a suitable prototype to build a Bosonic Dirac material only controlled by external field.