Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids

TL;DR

This paper explores higher rank tensor gauge theories in 3+1D spin liquids, revealing complex particle structures including immobile fractons and subspace-restricted particles, extending the understanding of gauge theories beyond conventional vector fields.

Contribution

It introduces the particle structure of higher rank U(1) tensor gauge theories, connecting them with fracton models and revealing new mobility restrictions of particles.

Findings

Particles can be fully immobile (fractons)

Some particles are restricted to lower-dimensional motion

Connections established with recent fracton models

Abstract

Spin liquids are conventionally described by gauge theories with a vector gauge field. However, there exists a wider class of spin liquids with higher rank tensors as the gauge variable. In this work, we focus on (3+1)-dimensional spin liquids described by U(1) symmetric tensor gauge theories, which have recently been shown to be stable gapless spin liquids. We investigate the particle structure of these tensor gauge theories and find that they have deep connections with the "fracton" models recently discovered by Vijay, Haah, and Fu. Tensor gauge theories have more conservation laws than the simple charge conservation law of rank 1 theories. These conservation laws place severe restrictions on the motion of particles. Particles in some models are fully immobile (fractons), while other models have particles restricted to motion along lower-dimensional subspaces.