Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory

TL;DR

This work elucidates how global and translational symmetries can enforce mobility restrictions in three-dimensional $\mathsf{U}(1)$ gauge theories, giving rise to fractonic matter through ASOC and symmetry-enriched topological order. It develops a systematic classification of $\mathsf{U}(1)$ gauge theories enriched by $\mathsf{U}(1)\times \mathbb{Z}^3$ symmetry, characterized by integer vectors $\mathbf{v}_e$ and $\mathbf{v}_m$, and identifies an anomaly-vanishing condition $\mathbf{v}_e\times\mathbf{v}_m=0$. The authors provide constructive realizations via gauged layered SPT phases and connect the resulting fracton physics to higher-rank tensor gauge theories and type-I fracton models like the X-cube through subsystem symmetry gauging. This framework unifies symmetry-enforced fractonic behavior in $3$D and offers practical routes to realize and manipulate fracton dynamics in quantum spin liquids and related systems. The insights have potential implications for robust quantum memory and the broader understanding of mobility constraints in quantum many-body physics.

Abstract

In this work we explore the interplay between global symmetry and the mobility of quasiparticle excitations. We show that fractonic matter naturally appears in a three dimensional U(1) gauge theory, enriched by global U(1) and translational symmetries, via the mechanism of anyonic spin-orbital coupling. We develop a systematic understanding of such symmetry-enforced mobility restrictions in terms of the classification of U(1) gauge theories enriched by U(1) and translational symmetries. We provide a unified construction of these phases by gauging layered symmetry-protected topological phases.

Figures (3)

• Figure 1: (a) Gauging $S_{\hat{x}}$ and $S_{\hat{y}}$ symmetry in a $\mathbb{Z}_N$ toric code model. Filled circles are original spins. Squares are gauge field spins, inside which the two dots represent gauge fields for $S_{\hat{x}}$ and $S_{\hat{y}}$ symmetries, respectively. (b) $e$ charge configuration created by Eq. \ref{['eqn:Zsite']}. (c) $e$ charge configuration created by Eq. \ref{['eqn:Zplaq']}. In (b) and (c) the numbers denote the corresponding $\mathbb{Z}_N$ gauge charge.
• Figure 2: Examples of the definition of $S_{\mu\nu}$ and $S_{\mu}$. The unit cell of the diamond lattice is depicted in (a) and (b). The operator $S_{\mu\nu}$ measures the electric field lines that go through the $\mu\nu$ direction. (a) As an example $S_{12}$ is shown. (b) An example $S_\mu$ operator which measures the electric dipole moment of the system along the ${\mathbf e}_\mu$ direction.
• Figure 3: A monopole-antimonopole pair in a layered SPT phase. A Dirac string penetrating layers of 2D SPT states is illustrated.