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

我们对Hubbard模型和三波段d-p模型进行了量子和变分蒙特卡罗模拟，以澄清高温超导体的物理性质。利用Gutzwiller ansatz对二维d-p模型进行的数值研究表明，在低掺杂和轻掺杂区域，不对称反铁磁态与超导性共存。该相图与最近对层状高温铜酸盐的实验结果一致。我们还对Bi-2212型带的二维t-t'-t"-U Hubbard模型进行了变分蒙特卡罗模拟，以检查最近在Bi-2212中通过扫描隧道显微镜观察到的4×4棋盘状状态的稳定性。我们发现以多q集为特征的键心四周期对角线和垂直自旋棋盘结构的共存状态是稳定的，并由4×4周期棋盘自旋调制组成。我们提出了一种基于量子蒙特卡罗方法和精确对角化方法来评估自旋磁化率和对磁化率的方法。利用量子蒙特卡罗方法，我们分别研究了半填充时的自旋磁化率和d波对称和s波对称的对磁化率对排斥和吸引相互作用的尺寸依赖性。我们已经证明了结果与Kosterlitz-Thouless跃迁的存在是一致的。

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.