Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

TL;DR

This paper introduces nonabelian higher-rank gauge theories based on volume-preserving diffeomorphisms, explaining phenomena in quantum Hall systems, vortex crystals, and ferromagnets through a unified symmetry framework.

Contribution

It constructs novel nonabelian higher-rank gauge theories from volume-preserving diffeomorphisms and applies them to various condensed matter systems, revealing new symmetry-based insights.

Findings

Derivation of GMP algebra and Wen-Zee term from the new gauge formalism

Effective actions for vortex and Wigner crystals derived using the gauge symmetry

Identification of fractonic behavior as a consequence of higher-rank gauge symmetry

Abstract

We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.