论文标题
统一拓扑顺序的退化
A degeneracy bound for homogeneous topological order
论文作者
论文摘要
我们介绍了均匀拓扑顺序的概念，大多数（如果不是全部）已知的拓扑顺序示例（包括量子旋转（Qudits））的拓扑顺序示例（即使不是全部）。该概念是基态子空间的条件，而不是在哈密顿量上，要求给出类似球的区域的收集，地面空间上的任何线性转换都可以由避免球状区域的操作员实现。对于具有同质拓扑顺序的系统，我们以任意封闭的riemannian dimension $ d $的方式得出了基态退化$ \ MATHCAL D $，它读取\ [\ log \ log \ log \ nogcal d \ lecμ（l/a）^{d-2}一个仅取决于歧管的等距类别的常数，而$μ$的常数仅取决于自由度的密度。如果$ d = 2 $，则常数$ c $是太空歧管的（demi）属。通过已知示例将该结合饱和到常数。
We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace, rather than on the Hamiltonian, and demands that given a collection of ball-like regions, any linear transformation on the ground space be realized by an operator that avoids the ball-like regions. We derive a bound on the ground state degeneracy $\mathcal D$ for systems with homogeneous topological order on an arbitrary closed Riemannian manifold of dimension $d$, which reads \[ \log \mathcal D \le c μ(L/a)^{d-2}.\] Here, $L$ is the diameter of the system, $a$ is the lattice spacing, and $c$ is a constant that only depends on the isometry class of the manifold, and $μ$ is a constant that only depends on the density of degrees of freedom. If $d=2$, the constant $c$ is the (demi)genus of the space manifold. This bound is saturated up to constants by known examples.
