Lifshitz point quantum critical spin liquids: Heisenberg versus easy-plane frustrated magnets

Full text: We solve the Lifshitz quantum critical problem for an easy plane antiferromagnet exactly. Using the solution we compare critical properties of the easy plane antiferromagnet with similar properties of the Heisenberg antiferromagnet. We find a qualitative difference between these two cases. The difference is in the span of the spin liquid phase: for the Heisenberg case the spin liquid occupies a domain on the phase diagram, for the easy plane case the domain shrinks to a point. The distinct properties are dictated by different character of topological excitations. In the Heisenberg case these are skyrmions, the energy of a skyrmion is zero at the critical point and hence skyrmions are relevant for the criticality. In the easy plane case the topological excitations are vortices, the energy of a vortex remains finite at the critical point and hence they are irrelevant for the criticality. (author)