我们计划在前期经验的基础上，采用变分蒙特卡罗方法，研究强关联电子体系几个有代表性的问题。我们计划研究的内容分为高温超导机理，量子自旋液体，以及莫特相变三个方面。在高温超导机理方面，我们计划研究共振价键背景上由反铁磁涨落散射造成的准粒子行为反常，探索共振价键理论对于电子配对和反铁磁关联的均衡描述，从动态涨落的角度研究赝能隙区主导的竞争序参量的形式和起源。在量子自旋液体方面，我们计划通过变分优化探索大能隙量子自旋液体实现的可能性，系统研究Kagome量子反铁磁体自旋液体基态的结构及其关于各种微扰的稳定性，研究三角晶格U（1）自旋液体分数化自旋激发关于规范涨落修正的稳定性。在莫特相变方面，我们计划采用基于slave rotor表示的新的变分波函数研究三角和Kagome晶格上两个模型的莫特相变，同时研究该方法在多轨道体系中的推广及其在轨道选择莫特相变研究中的应用。

We propose to study some key issues in the field of strongly correlated electron systems with our highly optimized variational Monte Carlo algorithms developed in recent years. The research topic covered by the our proposal can be divided into three parts, namely, high Tc mechanism, quantum spin liquid, and Mott transition. In the first part, we propose to study the quasiparticle anomaly in the high Tc cuprates induced by the scattering from AF spin fluctuation on the RVB background; to find a balanced description of SC pairing and AF correlation in the RVB framework, and to find out the form and origin of the dominant competing order in the pseudogap phase from a study of the dynamical spectrum on the RVB background. In the second part, we propose to search large gap spin liquid in realistic models with large scale variational optimization, to study systematically the structure of the spin liquid ground state of the Kagome QAF and its stability with respect to various perturbations, and to study the stability of the fractionalized spin excitation on the U(1) spin liquid with respect to gauge fluctuation correction. In the last part, we proposed to study the Mott transition with our new wave function for two models on the triangular and Kagome lattice, and to generalize the construction to multi-orbital systems with possible application on the study of orbital selective Mott transition.