We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the ${\mathbb{Z}}_4$- and ${\mathbb{Z}}_8$-symmetric free fractonic theories, we compute the time dynamics of several observables such as the two-point Green’s function, $⟨{\varphi }^2⟩$ condensate, energy density, and the dipole momentum. The time-dependent considerations highlight that the free fractonic theory breaks causality and exhibits instantaneous signal propagation, even if an additional relativistic term is included to enforce a speed limit in the system. We show that it is related to the fact that the Lieb-Robinson bound does not hold in the continuum limit of the fracton field theory, and the effective bounded speed of light does not emerge. For the theory in finite volume, we show that the fracton wave front acquires fractal shape with nontrivial Hausdorff dimension and argue that this phenomenon cannot be explained by a simple self-interference effect.

中文翻译：

---

分形场理论中的局部淬灭：Lieb-Robinson 界、非因果动力学和分形激励模式


我们研究分形场理论中局部扰动引起的不平衡动力学。对于 ${\mathbb{Z}}_4$ - 和 ${\mathbb{Z}}_8$ -对称自由分形理论，我们计算几个可观测量的时间动力学，例如两点格林函数， $⟨{\varphi }^2⟩$ 凝聚态、能量密度和偶极动量。与时间相关的考虑因素强调，自由分形理论打破了因果关系并表现出瞬时信号传播，即使包含附加的相对论项来强制系统中的速度限制也是如此。我们证明这与分形场理论的连续极限中Lieb-Robinson界不成立，并且有效有界光速不存在有关。对于有限体积理论，我们证明分形波前获得具有非平凡豪斯多夫维数的分形形状，并认为这种现象不能用简单的自干涉效应来解释。