Unification of pinch-points and half-moons in spin liquids*

Pinch-points — singularities in the momentum resolved structure factor — are arguably the most well-known signature of a U(1) spin liquid. As observed in various 2D and 3D lattice models, they imply divergence-free constraint on its effective magnetic field.

Another less celebrated, but also widely observed phenomenon in various spin liquids is half-moons in structure factors, i.e., circles with high intensity on opposite sides around Gamma points. Despite the long history since their discovery, a decent field-theoretical interpretation, as done for pinch-points, is still lacking.

In this talk, we propose a unifying theory for these two phenomena. We show that they arise from the dynamical properties of the divergence-free and curl-free components of the effective magnetic field respectively. While the divergence-free component dynamically decouples and forms a flat-band with pinch-points, the curl-free component carries perpendicular pinch-points and forms a dispersive band due to its non-trivial dynamical couplings.

We conclude, that “half-moons” are pinch-points on a dispersive band, seen on a constant energy cross-section. We propose that they can be observed in the quantum spin liquid material Ca₁₀Cr₇O₂₈.