Study of two-dimensional strongly correlated systems on the basis of Quantum Monte Carlo simulations and first principles calculations

为了阐明高温超导体的物理性质，我们对Hubbard模型和三带d-p模型进行了量子和变分蒙特卡罗模拟。利用Gutzwill er ansatz对二维d-p模型的数值研究表明，在低掺杂和轻掺杂区，无公度反铁磁态与超导电性共存。相图与最近层状高温铜酸盐的实验结果一致。我们还对具有Bi2212型能带的二维t-t‘-t“-U Hubbard模型进行了变分蒙特卡罗模拟，以考察最近用扫描隧道显微镜观察到的Bi2212中4×4棋盘态的稳定性。我们发现以键为中心的四周期对角和垂直自旋棋盘结构的共存态是稳定的，并且由4×4周期棋盘自旋调制组成。基于量子蒙特卡罗方法和精确对角化方法，我们提出了一种计算自旋磁化率和对磁化率等磁化率的方法。用量子蒙特卡罗方法研究了排斥和吸引相互作用的d波和S波对称性的半填充自旋极化率和对磁化率的尺寸依赖关系。我们的结果与Kosterlitz-Thouless转变的存在是一致的。

We have carried out quantum and variational Monte Carlo simulations for the Hubbard model and three-band d-p model to clarify the physics of high-temperature superconductors. Numerical studies of the two-dimensional d-p model by using the Gutzwiller ansatz have exhibited that the incommensurate antiferromagnetic state coexists with superconductivity in the under- and lightly doped regions. The phase diagram is consistent with recent experiments for layered high- temperature cuprates. We have also performed a variational Monte Carlo simulation on the two-dimensional t-t'-t"-U Hubbard model with Bi-2212-type band to examine the stability of a 4×4 checkerboard state which has been observed recently by scanning tunneling microscopy in Bi-2212. We have found that the coexistent state of bond-centered four-period diagonal and vertical spin-checkerboard structure characterized by a multi-Q set is stabilized and composed of 4×4 period checkerboard spin modulation. We have proposed a method to evaluate susceptibilities such as the spin susceptibility and pair susceptibility on the basis of quantum Monte Carlo methods and exact diagonalization method. Using quantum Monte Carlo method, we have examined the size dependence of the spin susceptibility at half filling and pair susceptibilities with d- and s-wave symmetries for the repulsive and attractive interactions, respectively. We have shown that the results are consistent with the existence of the Kosterlitz-Thouless transition.