生成函數的Kitaev模型譜函數研究

Abstract

在強相關系統的領域中，計算二維系統基態的2點函數是一項具有挑戰性的任務。這尤其適用於蜂巢結構的Kitaev模型，其中較大的鍵結維度和漢密爾頓量的複雜性，使得該模型不能僅使用實數進行計算。我們選擇在投影糾纏對態(PEPS)上的生成函數來計算有限晶格2點函數收縮，而無需手動進行容易出錯的張量網絡收縮，並在進行收縮時減小中間張量的大小。在這項工作中，我們將原始生成函數方法從實張量擴展到複張量微分，並計算蜂巢結構Kitaev模型的激發譜，靜態結構因子，和譜函數。對於激發譜，確定截斷Norm矩陣的正確維度一直是一個問題。我們提出利用譜函數和靜態結構因子之間的關係，找到符合總和規則的最佳截斷維度，並成功確定了蜂巢結構Kitaev模型等向點的截斷維度。

In the realm of strongly correlated systems, the calculation of the 2-point function of the underlying state in two-dimensional systems is a challenging task. This is especially true for the Honeycomb Kitaev Model, where the larger bond dimension and the fact that the model cannot be calculated using only real numbers due to the complexity of the Hamiltonian. Without approximating the two-dimensional system on the one-dimensional cylinder, we choose the generating function on Projected Entangled-Pair State(PEPS) to calculate the finite lattice 2-point function contraction without the need to conduct error-prone tensor network contraction by hand and reduce the size of intermediate tensor when doing the contraction. In this work, we extend the original generating function method from real tensor to complex tensor differentiation and calculate the excitation spectrum, static structure factor, and spectral function of the Honeycomb Kitaev model. For the excitation spectrum, it has been a problem to determine the correct dimension to truncate the Norm matrix. We purposed to exploit the relation between spectral function and static structure factor, finding the best truncation dimension that meets the sum rule, and we succeeded in determining the truncation dimension in the isotropic point of the Honeycomb Kitaev model.