Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry
Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry
复制标题
X立方分形拓扑序的量子场论和几何鲁棒简并性
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Yong Baek Kim
中科院分区：
文献类型：
--
作者：
K. Slagle;Yong Baek Kim
提出了一种分数阶拓扑有序X-立方体模型的量子场论描述。场论不是(也不可能是)拓扑量子场论(TQFT)，因为与X立方体模型不同，TQFT在连续的时空变换下是不变的(即对称的)。然而，该理论在保形群的某个子群下是不变的。我们描述了编织统计和基态简并是如何被场论再现的，以及X立方哈密顿量和场论如何最小限度地耦合到物质场。我们还证明了，即使在具有平凡拓扑的流形上，空间曲率也可以诱导对任意局部扰动稳定的基态简并！我们的形式可能允许描述其他分数场理论，其中唯一必要的输入是电荷密度的运动方程。
We propose a quantum field theory description of the X-cube model of fracton topological order. The field theory is not (and cannot be) a topological quantum field theory (TQFT), since unlike the X-cube model, TQFTs are invariant (i.e. symmetric) under continuous spacetime transformations. However, the theory is instead invariant under a certain subgroup of the conformal group. We describe how braiding statistics and ground state degeneracy are reproduced by the field theory, and how the the X-cube Hamiltonian and field theory can be minimally coupled to matter fields. We also show that even on a manifold with trivial topology, spatial curvature can induce a ground state degeneracy that is stable to arbitrary local perturbations! Our formalism may allow for the description of other fracton field theories, where the only necessary input is an equation of motion for a charge density.