**报告摘要： ** Quantum Monte Carlo (QMC) methods have become a key numerical technique for studying interacting quantum many-body systems in various areas. In this talk, I will concentrate on the auxiliary-field Quantum Monte Carlo (AFQMC) methods for the correlated fermion systems, and its most recent applications to 2D doped Hubbard model and Fermi gas with contact attraction. This talk will be separated into two parts, and they are summarized as follows.

I. In the first part, I will introduce the most recent numerical results obtained by the AFQMC methods in our group and related collaborations for both 2D doped Hubbard model and Fermi gas. Especially, for the 2D doped Hubbard model (only with nearest-neighbor hopping), the ground state is established as the stripe density wave ordered phase with filled stripes around 1/8-hole doping, and the d-wave superconductivity is absent. At finite temperatures, we have systematically studied the appearance, evolution and its behavior approaching the ground state of the spin and charge stripe density wave along with decreasing temperatures, while the d-wave pairing is also found to be suppressed. I will also show some results for the pseudogap behavior. For the 2D Fermi gas, we have computed the Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures, momentum distributions for fermions and Cooper pairs, contact parameter, and the Equation of State, which are very likely to be accessed by the future experiments.

II. In the second part, I will focus on the AFQMC algorithms for the correlated fermion systems, including the numerically exact Determinantal Quantum Monte Carlo method and the constrained-path approximation to control the minus sign/phase problem. Within the constrained-path approximation and its extension of phaseless approximation, the AFQMC methods have been widely applied to various fermionic system ranging from lattice models, Fermi gas to molecules and real metarials.

**报告人简介：** Yuan-Yao He got his PhD of Physics in Department of Physics, Renmin University of China in June 2018. In Sept. 2018, he moved to Center for Computational Quantum Physics (CCQ), Flatiron Institute (which is a division of Simons Foundation) in New York as a Flatiron Research Fellow. During his PhD, he focused on studying interacting topological insulators in lattice models using various quantum many-body numerical techniques, such as Exact Diagonalizations (ED) and Quantum Monte Carlo (QMC) methods. Since then, he mainly works on the developments and applications of finite-temperature QMC algorithms for correlated fermion systems, including the determinantal QMC method and the constrained-path QMC method which is used to control the sign problem. Most recently, he and his collaborators have dramatically reduced the computational cost of finite-temperature QMC methods by orders of magnitudes. This newest development allows for ab initio QMC simulations at finite temperatures for various fermion systems, ranging from lattice models to fermi gases, Quantum chemistry and real materials.