Pinch Point Singularities of Tensor Spin Liquids

TL;DR

This work addresses the identification of sharp experimental signatures for three-dimensional tensor $U(1)$ spin liquids, where emergent symmetric tensor gauge fields and fracton-like mobility constraints distinguish them from conventional vector $U(1)$ spin liquids. It develops the low-energy theory of rank-2 tensor gauge fields, derives universal pinch-point structures in spin-spin correlators for both scalar and vector charge realizations, and analyzes their classical and quantum limits. The authors predict a characteristic four-fold pinch-point pattern for rank-2 theories, distinct dispersion-dependent scaling, and specific low-temperature heat-capacity power laws for traceful and traceless variants, providing concrete diagnostic tools for neutron scattering and thermodynamics. These results offer a practical pathway to identify tensor Coulomb spin liquids in materials and guide experimental searches by linking universal tensor gauge theory properties to measurable signatures.

Abstract

Recently, a new class of three-dimensional spin liquid models have been theoretically discovered, which feature generalized Coulomb phases of emergent symmetric tensor $U(1)$ gauge theories. These "higher rank" tensor models are particularly intriguing due to the presence of quasi-particles 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 $U(1)$ 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.

Figures (1)

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