Low energy structure of classical spiral spin liquids

Spiral spin liquids are a class of spin liquids that have been experimentally discovered and theoretically studied in literature. However, a concrete physical picture of its spin liquid nature has not been established so far, considering that its zero-temperature ground states do not contain any local degeneracy. In this work we illustrate the low-energy structure of 2D spiral spin liquids, and reveal its connection to fracton and elasticity physics. We find that the local momentum vector can form new types of vortices in the system, which have very different properties from the commonly known spin vortices. The proliferation of such vortices leads the system into a liquid phase at low temperature. Furthermore, the effective theories of such vortices show that they are equivalent to quadrupoles of fractons/disclinations in rank-2 U(1) theory/elasticity. At very low temperature, the system freezes with these vortices forming a rigid network. Our work sheds light on the nature of classical spiral spin liquids, and also paves the way toward understanding the quantum limit of them.