Quantum Weyl-Heisenberg antiferromagnet

The Heisenberg model is a fundamental model of quantum magnetism that has been used to study a wide variety of physical systems, from high-Tc superconductors to spin liquids. In this work, we show that the introduction of anisotropic couplings in the square-lattice nearest-neighbor antiferromagnetic Heisenberg model can lead to the emergence of exotic topological states, including Weyl magnons. We study the model with anisotropic couplings using the spin-wave approximation and compute the edge spectrum and Berry connection vector, which show clear evidence of localizedtopological 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. Such states should be expected to occur naturally in most antiferromagnetic compounds which undergo structural transitions that reduce the point-group symmetry at lower temperature, and could also be realized in cold atom experiments.