Low-energy structure of spiral spin liquids

In this paper we identify a previously unexplored type of topological defect in spiral spin liquids---the momentum vortex---and reveal its dominant role in shaping the low-energy physics of such systems. Spiral spin liquids are a class of classical spin liquids featuring subextensively degenerate ground states. They are distinct from spin liquids on geometrically frustrated lattices, in which the ground-state degeneracy is extensive and connected by local spin flips. Despite a handful of experimental realizations and many theoretical studies, a concrete physical picture of their spin liquidity has not been established so far. In this paper, we study a 2D spiral spin liquid model to answer this question. We find that the local momentum vector field can carry topological defects in the form of vortices, which, however, have very different properties from the commonly known spin vortices. The fluctuations of such vortices lead the system into a liquid phase at intermediate temperatures. Furthermore, the effective low-energy theory of such vortices indicates their equivalence to quadrupoles of fractons in a rank-2 U(1) gauge theory or, alternatively, to quadrupoles of disclinations in elasticity theory. At very low temperatures, the system freezes into a glassy state in which these vortices form a rigid network with straight-line domain walls. Our paper sheds light on the nature of spiral spin liquids and also paves the way toward understanding their quantum limit.