When Diagrammatic Monte Carlo Meets Baym-Kadanoff algorithm: A Systematic Approach for Quantum Many-Body Dynamics

We introduce a bold diagrammatic Monte Carlo approach to study the linear response dynamics of quantum many-body systems. In order to describe the dynamics, it is vital to build the constant of motions into the structure of the Feynman diagrams used to calculate the many-body correlation functions. Using Baym-Kadanoff algorithm, we fix the conservation law for the two body correlation functions in the G²W skeleton diagrammatic expansion by introducing 3-point vertex functions. We then design a diagrammatic Monte Carlo method to self-consistently calculate high order diagrams for these vertex functions. The obtained two-body correlation functions, which obey all the conservation laws as well as several essential sum rules, give the access to the low-energy and long-wavelength response functions. We demonstrate that our method can be used to study the dynamical structure factor of frustrated Heisenberg model on the triangular lattice with a fermionization technique.