Pinch point singularities of tensor spin liquids

Recently, a new class of three-dimensional spin liquid models have been theoretically discovered, which feature generalized Coulomb phases of emergent symmetric tensor $U\left(1\right)$ gauge theories. These “higher rank” tensor models are particularly intriguing due to the presence of quasiparticles with restricted mobility, such as fractons. We investigate universal experimental signatures of tensor Coulomb phases. Most notably, we show that tensor Coulomb spin liquids (both quantum and classical) feature characteristic pinch point singularities in their spin-spin correlation functions, accessible via neutron scattering, which can be readily distinguished from pinch points in conventional $U\left(1\right)$ spin liquids. These pinch points can thus serve as a crisp experimental diagnostic for such phases. We also tabulate the low-temperature heat capacity of various tensor Coulomb phases, which serves as a useful additional diagnostic in certain cases.

Figure 1

The pinch point singularities of a conventional $U\left(1\right)$ spin liquid (left) have a characteristic twofold symmetry. In contrast, pinch points of the rank-2 tensor spin liquids (right) have a characteristic fourfold symmetry, which should allow for easy distinction in neutron-scattering data. [The two plots display $\langle E^x\left(q\right)E^y(-q)\rangle$ (left) and $\langle E^{xx}\left(q\right)E^{yy}(-q)\rangle$ (right), with cross sections taken in the $q_z=0$ plane.]

Figure 2

A microscopic model for the tensor gauge theories can be easily obtained via quantum rotors, with one quantum rotor on each plaquette of a cubic lattice, and three rotors on each site.