Title: Equation-of-Motion Series Expansion of Double-Time Green's Functions
Speaker: Tong Ninghua
Institute: Department of Physics, Renmin University of China
Time: 10:00am, Monday, Jan 25, 2016
Place: Room 520, New Building

Abstract：
Based on the equation of motion of Green's functions, a method is developed to expand a double-time Green's function into Taylor series of the parameter $\lambda$ in Hamiltonian $H=H_0 + \lambda H_1$. Here $H_0$ is the exactly solvable part and $H_1$ is regarded as the perturbation. We use the continued fraction to carry out the resummation of this series to produce spectral function without causality problem. Another problem of zero temperature divergence in the resummed GF is identified and solved by a self-consistent version of the series expansion. To demonstrate the implementation this method, both the weak as well as the strong coupling expansion are obtained for the Anderson impurity model to second order of $\lambda$. Using the self-consistent expansion and the continued fraction resummation method, we obtain improved strong-coupling expansion for the local density of states. The validity range and problems of this approach is discussed.