标题： 边缘上的分数量子霍尔效应 显示英文标题

标题： Fractons on the edge

摘要： 我们发展了二维分形子系统边缘激发的理论，并阐明了它们与体输运性质和体激发量子统计之间的联系。 我们考虑的系统具有固定的点电荷，其偶极子仅能沿着与其矩垂直的线移动，以及自由移动的四极子和更高阶多极子，实现了体分形子对分数量子霍尔相的类比。 我们证明，只有在两种情况下才能获得两个体激发之间的量化编织相：当一个点四极子绕着一个固定点电荷编织时，或者当两个非正交点偶极子相互编织时。 系统中边界边缘的存在导致$\textit{two}$种无能隙边缘激发模式，其中一种是分形子模式，具有固定的电荷和纵向偶极子，另一种是非分形子模式，由横向偶极子组成。 我们推导了分形子边缘模式的新电流代数。 此外，研究局部边缘到边缘的隧穿效应对这些模式的影响，我们发现这种过程是一个相关的扰动，暗示了边缘变形的可能性。 显示英文摘要

摘要： We develop a theory of edge excitations of fractonic systems in two dimensions, and elucidate their connections to bulk transport properties and quantum statistics of bulk excitations. The system we consider has immobile point charges, dipoles constrained to move only along lines perpendicular to their moment, and freely mobile quadrupoles and higher multipoles, realizing a bulk fractonic analog of fractional quantum Hall phases. We demonstrate that a quantized braiding phase between two bulk excitations is obtained only in two cases: when a point quadrupole braids around an immobile point charge, or when two non-orthogonal point dipoles braid with one another. The presence of a boundary edge in the system entails $\textit{two}$ types of gapless edge excitation modes, one that is fractonic with immobile charges and longitudinal dipoles, and a second non-fractonic mode consisting of transverse dipoles. We derive a novel current algebra of the fractonic edge modes. Further, investigating the effect of local edge-to-edge tunneling on these modes, we find that such a process is a relevant perturbation suggesting the possibility of edge deformation.