Flatiron Seminar Series: Jason Kaye

Title: The Green’s function view of interacting quantum physics

Abstract: The central challenge in simulating the physics of many interacting quantum particles is the exponential growth of the many-body state space dimension with respect to the number of possible states of a single particle. Green’s function methods offer an alternative to the standard wavefunction-based picture of quantum physics, suggesting systematic strategies to approximate the effects of particle interactions to obtain a computationally tractable description of observables.

This talk will give a pedagogical introduction to some basic characters of quantum many-body theory, including creation and annihilation operators, the Hubbard model, the single-particle Green’s function, the self-energy, and dynamical mean-field theory (DMFT). We will see that the single-particle Green’s function of many-body theory naturally generalizes its more familiar classical counterpart, and that it provides a practical link with experiment via the spectral function. We will then describe a new method of computing the Green’s function within DMFT, which uses a simple and well-known trick from computational mathematics, sum-of-exponentials expansion and separation of variables, to evaluate the Feynman diagrams arising from perturbation theory.