1.强关联体系是凝聚态物理领域中被大家所公认的一个最为复杂和最具有挑战性的研究领域，它涉及到大量的新奇而有趣的物理现象并具有非常丰富的物理内涵。该领域的理论研究往往与实验研究密切关联，所涉及到的材料主要包括高温铜氧化物超导体（Patrick A Lee, From high temperature superconductivity to quantum spin liquid: progress in strong correlation physics, Rep. Prog. Phys. 71, 012501 (2008)）和铁基超导体（G. R. Stewart, Superconductivity in iorn compounds, Rev. Mod.Phys. 83, 1589 (2011)）等。我们利用数值方法来研究掺杂过程所引入的杂质无序对上述强关联体系的物理性质的影响，并关注由无序所诱导的Anderson金属-绝缘体转变（E. Abrahams, 50 years of Anderson localization, World Scientific, 2010）与强相互作用所导致的Mott金属-绝缘体转变（M. Imada etal., Metal-insulator transitions, Rev. Mod. Phys. 70, 1039 (1998)）如何来共同构建出全景相图等重要的基本物理问题。

2.在钙钛矿结构过渡族金属氧化物强关联体系中，自旋序、电荷序、轨道序和晶格结构序等的共同作用可以使得体系呈现出许多不同的电子状态和丰富多彩的物理性质（M. B. Salamon and M. Jaime, The physics of manganites: Structure and transport, Rev. Mod. Phys. 73, 583 (2001）），因此近年来人们对轨道自由度能够引起哪些新奇的物理现象非常关注，例如有轨道选择的金属-绝缘体转变（V. I. Anisimov, et al., Eur. Phys. J. B 25, 191 (2002)）和轨道序等。动力学平均场理论（A. Georges, et al., Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996); G. Kotliar, et al., Electronic structure calculations with dynamical mean-field theory, Rev. Mod. Phys. 78, 865 (2006); T. Maier, et al., Quantum cluster theories, Rev. Mod. Phys. 77, 1027 (2005)）是近几年针对强关联体系而发展起来的一套非常成功的数值方法。我们将发展这一方法来研究多能带强关联体系中的巡游磁性和量子相变等问题。

3.其它一些感兴趣的研究方向：新型二维材料（石墨烯、范德瓦尔斯磁性材料和过渡金属硫族化合物等）的新奇物性及无序效应的理论研究。

1. Yu Ni, et al., Electronic correlation-driven orbital polarization transitions in the orbital-selective Mott compound Ba2CuO4−δ, Physcal Review B 103, 214510 (2021) (http://doi.org/10.1103/PhysRevB.103.214510)

2. Yuekun Niu, et al., Doublon-holon excitations split by Hund’s rule coupling within the orbital-selective Mott phase, Physical Review B 100, 075158 (2019) (http://doi.org/10.1103/PhysRevB.100.075158)

3. Zhao Yang-Yang. et al., Anderson localization effect on Mott phase in 1T-TaS2, Acta Physica Sinica, 66, 057101 (2017) (http://dx.doi.org/10.7498/aps.66.057101)

4. Jian Sun, et al., Disorder driven superconductor-insulator transition in inhomogeneous d-wave superconductor, Science China-Physics, Mechanics & Astronomy 59, 617401 (2016) (https://link.springer.com/article/10.1007/s11433-015-5713-4)

5. Yang Liu, et al., Localization and orbital selectivity in iron-based superconductors with Cu substitution, Physical Review B 92, 155146 (2015) (http://doi.org/10.1103/PhysRevB.92.155146)

6. Zhuoling Jiang, et al., Band gap oscillation and novel transport property in ultrathin chiral graphene nanoribbons, Physica B 464, 61 (2015) (http://doi.org/10.1016/j.physb.2015.02.003)

7. Long He, et al., Self-consistent calculations of the effects of disorder in d-wave and s-wave superconductors, J. Korean Phys. Soc. 63, 2223 (2013) (https://link.springer.com/article/10.3938%2Fjkps.62.2223)

8. Yun Song, et al., The effects of disorder and interactions on the Anderson transition in doped graphene, J. Phys.: Condens. Matter 23, 205501 (2011) (http://iopscience.iop.org/0953-8984/23/20/205501)

9. Yun Song, et al., Dynamical mean field study of the two-dimensional disordered Hubbard model, Physical Review B 77, 054202
(2008) (http://doi.org/10.1103/PhysRevB.77.054202)

10. Yun Song, et al., Geometrically Averaged Density of States as a Measure of Localization, Physical Review B 76, 045105 (2007) (http://doi.org/10.1103/PhysRevB.76.045105)