Hubbard 模型是凝聚态强关联物理研究的基本模型。现在，越来越多的研究 结果表明，Hubbard 模型及其推广具有十分丰富的基态和低能物理性质，有各种各样的 emergent 现象。本项目从两个方面着手探讨这类模型重要的基态性质和emergent 现象：（1） 引入自旋依赖和自旋翻转的hopping 项，研究各种二维晶格中费米子模型的相图，探讨具有 不同规范对称性自旋液体态。（2）在多带模型中，引入一些推广的Hubbard 相互作用项，可 以发现在一些给定的格子上，emergent 低能有效理论是一些非常重要场论模型，例如，2＋1维量子电动力学，甚至非阿贝尔规范理论，这样，我们可以研究这类模型中的lattice 和连续极限的禁闭问题，这对高能物理中的夸克禁闭问题有很好的借鉴作用。

Hubbard models are the fundamental models to study the strongly correlated systems in condensed matter physics. Many research results show that there are fruitful physical properties of the ground states and low-lying excitations for this type of models. Various interesting phenomena can emerge. In this project, we would like to study the ground states and emergent phenomena in the following two aspects: (1) introducing the hopping terms with spin-dependent and spin-flip, we study the phase diagrams of the models in several two-dimensional lattices. Especially, we search for the spin liquid states with different gauge symmetries. (2) In multi-band models, we consider generalized Hubbard interacting potentials. It is expected that the emergent low-lying effective theory may be very important field theory models, e.g, 2+1 QED and even non-abelian gauge theory. Thus, we can study the confinement problem in the lattice model as well as the continuum limit. These studies may be helpful to understand the quark confinement in QCD.