论文标题
关于张量网络中拓扑顺序的稳定性
On the stability of topological order in tensor network states
论文作者
论文摘要
我们构建了3D复型代码接地状态的张量网络表示，该表示与生成一组均匀的本地张量扰动，包括那些不映射到物理希尔伯特空间上的本地操作员的扰动。通过将扰动张量网络的相图映射到3D ISING仪表理论的相位图来建立稳定性，该量表理论具有非零的有限温度跃迁。更普遍地，我们发现拓扑张量网络状态的稳定性取决于其虚拟对称性的形式以及破坏这些对称性的虚拟操作员产生的拓扑激发。特别是，发现3D旋转代码基态的双重表示，以及X-Cube和Cubic Code接地状态的表示形式，该状态是由该操作员创造的类似点的激发，这是不稳定的。
We construct a tensor network representation of the 3d toric code ground state that is stable to a generating set of uniform local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The stability is established by mapping the phase diagram of the perturbed tensor network to that of the 3d Ising gauge theory, which has a non-zero finite temperature transition. More generally, we find that the stability of a topological tensor network state is determined by the form of its virtual symmetries and the topological excitations created by virtual operators that break those symmetries. In particular, a dual representation of the 3d toric code ground state, as well as representations of the X-cube and cubic code ground states, for which point-like excitations are created by such operators, are found to be unstable.
