Proximate Dirac spin liquid in honeycomb lattice J₁-J₃ XXZ model: Numerical study and application to cobaltates

The honeycomb cobaltates, initially proposed as candidate Kitaev quantum magnets, have been shown recently to be described instead by a pseudospin-1/2 easy-plane spin Hamiltonian with nearest neighbor ferromagnetic (FM) exchange J₁ being frustrated by antiferromagnetic third-neighbor exchange J₃ and weaker compass anisotropies. Using exact diagonalization and density-matrix renormalization group (DMRG) calculations, we show that this model exhibits FM order at small J₃/J₁ and zig-zag (ZZ) order at large J₃/J₁, separated by an intermediate phase, which is shown to exhibit spin-liquid-like correlations in DMRG, although weak broken symmetries cannot be precluded. Using a modified parton mean field theory and variational Monte Carlo on Gutzwiller projected wavefunctions, we show that the optimal FM and ZZ orders as well as the intermediate SL-like state are proximate to a `parent' Dirac spin liquid (SL). This Dirac SL is shown to capture the broad continuum in the temperature and magnetic field dependent terahertz spectroscopy of BaCo₂(AsO₄)₂ (BCAO), and the reported low temperature metallic thermal conductivity in Na₂Co₂TeO₆ (NCTO) and BCAO. We generalize our results to discuss neutron scattering and other spectroscopic signatures of the proximate Dirac SL.