论文标题
$ k $ layer ising coric代码中的量子相变
Quantum phase transitions in the $K$-layer Ising toric code
论文作者
论文摘要
我们调查了$ k $ layer ising toric代码的量子相图，该代码对应于$ k $层的二维复曲面代码，并通过Ising Interactions结合使用。对于小ising交互，系统显示$ \ mathbb {z} _2^k $拓扑顺序来自每一层中的复曲面代码，该系统显示$ \ MATHBB {z} _2 $ topogical Order Ordogical Order Order Order Order Order Order Order Ordogical Order Ordogical Order in High-assion Limit。通过在$ k^{\ rm th} $中得出有效的低能模型，证明了后者的一般$ k $ - 订购退化扰动理论，该理论作为一个有效的各向异性单层旋转曲线代码，该代码在集体伪旋转方面，指的是指隔离的隔离式链条链链的两种地面。对于特定情况，$ k = 3 $和$ k = 4 $我们应用高阶系列扩展，以在低和高效率上确定差距系列。基本能量差距的外推给出了令人信服的证据，即地面相图由两个$ k $分隔两种类型的拓扑顺序的3D ising*通用类中的单个量子临界点，这与以前的BiLayer issing Isstric Code的发现是一致的。
We investigate the quantum phase diagram of the $K$-layer Ising toric code corresponding to $K$ layers of two-dimensional toric codes coupled by Ising interactions. While for small Ising interactions the system displays $\mathbb{Z}_2^K$ topological order originating from the toric codes in each layer, the system shows $\mathbb{Z}_2$ topological order in the high-Ising limit. The latter is demonstrated for general $K$ by deriving an effective low-energy model in $K^{\rm th}$-order degenerate perturbation theory, which is given as an effective anisotropic single-layer toric code in terms of collective pseudo-spins 1/2 refering to the two ground states of isolated Ising chain segments. For the specific cases $K=3$ and $K=4$ we apply high-order series expansions to determine the gap series in the low- and high-Ising limit. Extrapolation of the elementary energy gaps gives convincing evidence that the ground-state phase diagram consists of a single quantum critical point in the 3d Ising* universality class for both $K$ separating both types of topological order, which is consistent with former findings for the bilayer Ising toric code.
