Quantum Weyl-Heisenberg antiferromagnet

Beginning from the conventional square-lattice nearest-neighbor antiferromagnetic Heisenberg model, we allow the Jx and Jy couplings to be anisotropic, with their values depending on the bond orientation. The emergence of anisotropic, bond-dependent couplings should be expected to occur naturally in most antiferromagnetic compounds which undergo structural transitions that reduce the point-group symmetry at lower temperature. Using the spin-wave approximation, we study the model in several parameter regimes by diagonalizing the reduced Hamiltonian exactly and computing the edge spectrum and Berry connection vector, which show clear evidence of localized topological charges. We discover phases that exhibit Weyl-type spin-wave dispersion, characterized by pairs of degenerate points and edge states, as well as phases supporting lines of degeneracy. We also identify a parameter regime in which there is an exotic state hosting gapless linear spin-wave dispersions with different longitudinal and transverse spin-wave velocities.