We revisit a model for gapped fractonic order in (2+1) dimensions (a symmetric-traceless tensor gauge theory with conservation of dipole and trace-quadrupole moments described in \cite{Prem:2017kxc}) and compute its ground-state entanglement entropy on $\mathbb R^2$. Along the way, we quantize the theory on open subsets of $\mathbb R^2$ which gives rise to gapless edge excitations that are Lifshitz-type scalar theories. We additionally explore varieties of gauge-invariant extended operators and rephrase the fractonic physics in terms of the local deformability of these operators. We explore similarities of this model to the effective field theories describing quantum Hall fluids: in particular, quantization of dipole moments through a novel compact symmetry leads us to interpret the vacuum of this theory as a dipole condensate atop of which dipoles with fractionalized moments appear as quasi-particle excitations with Abelian anyonic statistics. This interpretation is reflected in the subleading ``topological entanglement" correction to the entanglement entropy. We extend this result to a series of models with conserved multipole moments.

中文翻译：

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偶极子量子霍尔流体中的纠缠

我们重新审视了 (2+1) 维中的间隙分形阶数模型（一种对称无迹张量规范理论，在 \cite{Prem:2017kxc} 中描述了偶极矩和迹四极矩守恒）并计算其基态纠缠熵在 $\mathbb R^2$ 上。在此过程中，我们量化了关于 $\mathbb R^2$ 的开放子集的理论，这产生了 Lifshitz 型标量理论的无间隙边缘激发。我们还探索了各种规范不变扩展算子，并根据这些算子的局部变形能力重新表述了分形物理学。我们探索该模型与描述量子霍尔流体的有效场论的相似之处：特别是，通过新颖的紧凑对称性对偶极矩进行量化，使我们将这一理论的真空解释为偶极凝聚体，其上具有分数化矩的偶极子表现为具有阿贝尔任意子统计的准粒子激发。这种解释反映在对纠缠熵的次要“拓扑纠缠”校正中。我们将此结果扩展到一系列具有守恒多极矩的模型。