论文标题
通过映射到随机步行
Exact bounds on the energy gap of transverse-field Ising chains by mapping to random walks
论文作者
论文摘要
基于Iglói，Turban和Rieger发现的连续时间随机步行的关系[Phys。 Rev. e {\ bf 59}，1465（1999）]，我们在开放式横向场iSing链的最低能量间隙中得出了精确的下限和上限，这些链在参数中是显式的，通常对可能随机的随机耦合和磁场的任意集有效。在同质链和具有不相关参数的随机链中，发现上下边界在铁磁相中和关键点都显示出相同的有限尺寸缩放尺寸，这表明了这些边界推断关键差距的正确有限尺寸尺度的能力。将边界应用于具有耦合场相关性的随机横向局部ising链，该模型与绝热量子计算相关，间隙的有限尺寸缩放与独立随机变量的总和相关。我们确定模型的临界动力学指数，并揭示了特殊点上对数校正的存在。
Based on a relationship with continuous-time random walks discovered by Iglói, Turban, and Rieger [Phys. Rev. E {\bf 59}, 1465 (1999)], we derive exact lower and upper bounds on the lowest energy gap of open transverse-field Ising chains, which are explicit in the parameters and are generally valid for arbitrary sets of possibly random couplings and fields. In the homogeneous chain and in the random chain with uncorrelated parameters, both the lower and upper bounds are found to show the same finite-size scaling in the ferromagnetic phase and at the critical point, demonstrating the ability of these bounds to infer the correct finite-size scaling of the critical gap. Applying the bounds to random transverse-field Ising chains with coupling-field correlations, a model which is relevant for adiabatic quantum computing, the finite-size scaling of the gap is shown to be related to that of sums of independent random variables. We determine the critical dynamical exponent of the model and reveal the existence of logarithmic corrections at special points.
