第一性原理计算方法开发，机器学习势函数构建，机器学习结构搜索，强关联量子材料设计

代表性成果：
(1)在VASP软件中开发了能够准确计算高达上百个原子体系准粒子能量的快速高效的GW方法及能够计算固体材料准粒子能量的完全自洽的GW方法；参与开发了第一性原理计算电子相关作用的约束随机相近似cRPA方法以及GW方法与动力学平均场理论DMFT的结合
(2)提出了非线性LSDA+U模型，更正了传统线性LSDA+U模型在处理非线性磁体系上的错误； 基于模型介电函数统一了现有杂化密度泛函理论，并提出了基于时间依赖的密度泛函理论和模型介电函数计算材料吸收谱更为有效的新方法
(3)提出了利用自适应机器学习方法结合Δ-机器学习方法来有效构建超越密度泛函理论框架下的高精度的原子间力场
(4)揭示了强关联自旋轨道耦合的5d过渡金属Ir化物和Os化物的新奇物性机理
代表论文
(1)Cubic scaling GW: towards fast quasiparticle calculations，Peitao Liu*, Merzuk Kaltak, Jiri Klimes, and Georg Kresse, Physical Review B 94, 165109 (2016) (PRB Editors' Suggestions)
(2)Beyond the quasiparticle approximation: Fully self-consistent GW calculations, Manuel Grumet, Peitao Liu*, Merzuk Kaltak, Jiří Klimeš, and Georg Kresse*, Phys. Rev. B 98, 155143 (2018). (PRB Editors' Suggestions)
(3)Parameterisation of LSDA+U for non-collinear magnetic configurations: Multipolar magnetism in UO2, S. L. Dudarev*,†, P. Liu†, D. A. Andersson, C. R. Stanek, T. Ozaki and C. Franchini*, Phys. Rev. Materials 3, 083802 (2019).
(4)Merging GW with DMFT and non-local correlations beyond, Jan M. Tomczak, Peitao Liu, Alessandro Toschi, Georg Kresse and Karsten Held*, Eur. Phys. J. Special Topics 226, 2565 (2017) (Topical review)
(5)Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO, Peitao Liu*, Cesare Franchini, Martijn Marsman, and Georg Kresse, J. Phys.: Condens. Matter 32, 015502 (2019).
(6)Anisotropic magnetic couplings and structure-driven canted to collinear transitions in Sr2IrO4 by magnetically constrained noncollinear DFT, Peitao Liu, S. Khmelevskyi, B. Kim, M. Marsman, D. Li, X-Q Chen, D.D. Sarma, G. Kresse, and C. Franchini*, Physical Review B 92, 054428 (2015).
(7)Electron and hole doping in the relativistic Mott insulator Sr2IrO4: a first-principles study using band unfolding technique, Peitao Liu, Michele Reticcioli, Bongjae Kim, Alessandra Continenza, Georg Kresse, D.D. Sarma, Xing-Qiu Chen, and Cesare Franchini*, Physical Review B 94, 195145 (2016).
(8)Relativistic GW+BSE study of the optical properties of Ruddlesden-Popper iridates, Peitao Liu*, Bongjae Kim, Xing-Qiu Chen, D. D. Sarma, Georg Kresse, and Cesare Franchini, Phys. Rev. Materials 2, 075003 (2018).
(9)Advanced first-principles modeling of relativistic Ruddlesden-Popper strontium iridates, Peitao Liu and Cesare Franchini*, Appl. Sci. 11, 2527 (2021).
(10)α-β phase transition of zirconium predicted by on-the-fly machine-learned force field, Peitao Liu*, Carla Verdi, Ferenc Karsai, and Georg Kresse, Phys. Rev. Materials 5, 053804 (2021).
(11)Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory, Peitao Liu*, Carla Verdi, Ferenc Karsai, and Georg Kresse, (arXiv:2109.06282v1(2020)).
(12)Osmates on the verge of a Hund’s-Mott transition: The different fates of NaOsO3 and LiOsO3, Daniel Springer, Bongjae Kim, Peitao Liu, Sergii Khmelevskyi, Severino Adler, Massimo Capone, Giorgio Sangiovanni, Cesare Franchini, and Alessandro Toschi*, Phys. Rev. Lett. 125, 166402 (2020).
(13)Accurate optical spectra through time-dependent density functional theory based on model-dielectric-dependent hybrid functionals, Alexey Tal*, Peitao Liu, Georg Kresse, and Alfredo Pasquarello, Phys. Rev. Research 2, 032019(R) (2020) (Rapid Communications)
(14)Thermodynamic properties by on-the-fly machine-learned interatomic potentials: thermal transport and phase transitions of zirconia, Carla Verdi*, Ferenc Karsai, Peitao Liu, Ryosuke Jinnouchi, and Georg Kresse (npj Computational Materials, 7, 156, 2021).
Energetics of the coupled electronic-structural transition in the rare-earth nickelates, Alexander Hampel*, Peitao Liu, Cesare Franchini and Claude Ederer*, npj Quantum Materials 4, 5 (2019).