Pinch-line spin liquids as layered Coulomb phases and applications to cubic models

TL;DR

This paper introduces a framework for designing layered spin liquids with pinch-line singularities, expanding the understanding of emergent gauge fields and fractonic matter, supported by simulations and theoretical analysis.

Contribution

It proposes a simple, versatile framework for creating pinch-line spin liquids in layered structures, connecting emergent electric fields to singularities and exploring new fractonic phases.

Findings

Framework successfully models layered spin liquids with pinch lines

Simulations confirm the theoretical predictions

Continuous variation of gauge field rank along pinch lines

Abstract

Spin liquids form fluctuating magnetic textures which have to obey certain rules imposed by frustration. These rules can often be written in the form of a Gauss law, indicating the local conservation of an emergent electric field. In reciprocal space, these emergent Gauss laws appear as singularities known as pinch points, that are accessible to neutron-scattering measurements. But more exotic forms of electromagnetism have been stabilized in spin liquids, and in a few rare instances, these zero-dimensional singularities have been extended into one-dimensional pinch lines. Here we propose a simple framework for the design of pinch-line spin liquids in a layered structure of two-dimensional algebraic spin liquids. A plethora of models can be build within this framework, as exemplified by several concrete examples where our theory is confirmed by simulations, and where the rank of the tensorial gauge field is continuously varied along the pinch line, opening new avenues in fractonic matter. Then we use our framework to understand how the evolution of the singularity pinch point along the pinch line can be understood as the interference pattern of two emergent electric fields. Finally, we apply our intuition on these emergent electric fields in real space to generic pinch line models beyond our layered framework, and revisit the recently proposed pinch line model on the octochlore lattice.