Low energy structure of spiral spin liquids

TL;DR

This paper uncovers a new type of topological defect called momentum vortices in spiral spin liquids, revealing their crucial role in low energy physics and phase transitions, and linking them to fracton theories.

Contribution

It introduces the concept of momentum vortices in spiral spin liquids and explores their impact on the system's low energy behavior and phase structure.

Findings

Momentum vortices are topological defects in spiral spin liquids.

Fluctuations of these vortices induce a liquid phase at intermediate temperatures.

At low temperatures, vortices form a rigid network leading to a glassy state.

Abstract

In this work 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 sub-extensively 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 work, 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 work sheds light on the nature of spiral spin liquids and also paves the way toward understanding their quantum limit.