论文标题
量子横向场模型的蠕虫 - 叠加型模拟
Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model
论文作者
论文摘要
我们应用蠕虫算法以在路径融合表示中模拟量子横向视野模型，该模型的膨胀基础被视为沿外部场方向的旋转分量。在这样的表示形式中，可以将配置视为一组由“扭结”构建的非交流环，用于成对相互作用和旋转（或-up）假想时间段。观察到旋转环的包装概率是表征圆环上环拓扑的无量纲数量，可以显示出小的有限尺寸校正，并在两个维度（2D）中获得高精度的临界点为$ h_c \！ = \！ 3.044 \，330（6）$，比现有结果大大改善，几乎不包括最佳的$ H_C \！ = \！ 3.044 \，38（2）$。在关键时期，环的分形尺寸估计为$ d _ {\ ell \ downarrow}（1 {\ rm d}）\！ = \！ 1.37（1）\！ \大约！ 11/8 $和$ d _ {\ ell \ downarrow}（2 {\ rm d}）\！ = \！ 1.75（3）$，分别与经典2D和3D O（1）循环模型的$一致。一个有趣的功能是，在一个维度（1D）中，旋转和-up循环在整个无序阶段（$ 0 \！\！\ leq \！h \！ = \！ 1.750（7）$与船体尺寸$ d _ {\ rm h} \！ = \！关键2D渗透集群的7/4 $。当前的蠕虫算法可以应用于模拟其他量子系统，例如与配对相互作用的硬核玻色子模型。
We apply a worm algorithm to simulate the quantum transverse-field Ising model in a path-integral representation of which the expansion basis is taken as the spin component along the external-field direction. In such a representation, a configuration can be regarded as a set of non-intersecting loops constructed by "kinks" for pairwise interactions and spin-down (or -up) imaginary-time segments. The wrapping probability for spin-down loops, a dimensionless quantity characterizing the loop topology on a torus, is observed to exhibit small finite-size corrections and yields a high-precision critical point in two dimensions (2D) as $h_c \! =\! 3.044\, 330(6)$, significantly improving over the existing results and nearly excluding the best one $h_c \! =\! 3.044\, 38 (2)$. At criticality, the fractal dimensions of the loops are estimated as $d_{\ell \downarrow} (1{\rm D}) \! = \! 1.37(1) \! \approx \! 11/8 $ and $d_{\ell \downarrow} (2{\rm D}) \! = \! 1.75 (3)$, consistent with those for the classical 2D and 3D O(1) loop model, respectively. An interesting feature is that in one dimension (1D), both the spin-down and -up loops display the critical behavior in the whole disordered phase ($ 0 \! \leq \! h \! < \! h_c$), having a fractal dimension $d_{\ell} \! = \! 1.750 (7)$ that is consistent with the hull dimension $d_{\rm H} \! = \! 7/4$ for critical 2D percolation clusters. The current worm algorithm can be applied to simulate other quantum systems like hard-core boson models with pairing interactions.
