标题： 局域扰动下具有开放边界的拓扑码中的量子相变纠缠和保真度 显示英文标题

标题： Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries

摘要： 我们研究了在局部扰动（如局域磁场和伊辛型自旋-自旋相互作用）下，Kitaev码中发生的拓扑到非拓扑的量子相变（QPTs），并使用保真度敏感度（FS）和纠缠作为探测工具。 我们假设该码嵌入在一个高度为$M$、周长为$D$且具有$M\ll D$的宽圆柱体表面上。 我们展示了在QPT处FS的幂律发散，并通过有限尺寸标度分析确定了量子临界点（QCPs）。 我们通过将受扰动的Kitaev码映射到具有最近邻和次近邻相互作用的二维伊辛模型，并使用量子蒙特卡罗技术计算单个位点磁化强度作为序参量来验证这些结果。 我们还指出，在仅施加伊辛相互作用的情况下，Kitaev梯子中QPT的发生存在奇偶二分法，这取决于$D$的奇偶值。 我们的结果还表明，如果在某一方向上使边界开放，Kitaev码的拓扑相对局部扰动具有更高的鲁棒性。 我们进一步考虑了一个专门设计的局部纠缠见证算符，以捕捉码的垂直非平凡环上的可定位纠缠的下限。 我们证明了该见证算符期望值的一阶导数在QPT处表现出对数发散，并进行了有限尺寸标度分析。 我们在具有开放边界的局部扰动颜色码的情况下，也展示了适当构造的见证算符期望值的类似行为。 显示英文摘要

摘要： We investigate the topological-to-non-topological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations in the form of local magnetic field and spin-spin interactions of the Ising-type using fidelity susceptibility (FS) and entanglement as the probes. We assume the code to be embedded on the surface of a wide cylinder of height $M$ and circumference $D$ with $M\ll D$. We demonstrate a power-law divergence of FS across the QPT, and determine the quantum critical points (QCPs) via a finite-size scaling analysis. We verify these results by mapping the perturbed Kitaev code to the 2D Ising model with nearest- and next-nearest-neighbor interactions, and computing the single-site magnetization as order parameter using quantum Monte-Carlo technique. We also point out an odd-even dichotomy in the occurrence of the QPT in the Kitaev ladder with respect to the odd and even values of $D$, when the system is perturbed with only Ising interaction. Our results also indicate a higher robustness of the topological phase of the Kitaev code against local perturbations if the boundary is made open along one direction. We further consider a local entanglement witness operator designed specifically to capture a lower bound to the localizable entanglement on the vertical non-trivial loop of the code. We show that the first derivative of the expectation value of the witness operator exhibits a logarithmic divergence across the QPT, and perform the finite-size scaling analysis. We demonstrate similar behaviour of the expectation value of the appropriately constructed witness operator also in the case of locally perturbed color code with open boundaries.