二維量子反鐵磁中的挫折性交互作用

Abstract

We use the Stochastic Series Expansion Quantum Monte Carlo (SSE QMC) method [1, 2, 3] to study the impurity problem in the CuO2 plane of high-Tc superconducting materials. This plane is a 2D antiferromagnetic square lattice, at which the superconductivity usually occurs. Doping nonmagnetic impurities to replace Cu ions in this plane exhibits very strong electronic behavior. Hence the impurity problem forms an important class of strongly correlated electron systems. In the presence of impurities in the CuO2 plane, from previous study [4], people already know that there are staggered moments localized around impurity sites. If the impurity concentration increases, both the theoretical and numerical studies [5, 6, 7] suggested that, at some critical density, there is a vanishing staggered magnetization, which is a suitable order parameter in this antiferromagnetic system. However, there is a discrepancy between the theoretical prediction and the experimental results [8] at high impurity concentration. The numerical and theoretical results are slightly higher than the experimental one. The discrepancy mentioned above leads us to consider the impurity-induced frustration interaction [9, 10] in the system. Since frustration will further destroy the order of the system, this frustrated interaction may account for this discrepancy. In this thesis, numerical results for the staggered magnetization and the Knight shifts are presented. In the final part we show numerical results that support our suggestion that frustrations will further destroy the order of a system. Also, SSE QMC faces the notorious “sign problem” [11, 12] when dealing with frustrated systems, so the numerical results about the sign problem are also briefly discussed.