Diagrammatic Monte Carlo for the Hubbard Model

In this talk, I will present recent developments of the diagrammatic Monte Carlo method applied to the Hubbard model. Diagrammatic Monte Carlo methods are based on the construction of a perturbation series for physical observables. They face two main challenges: The first challenge is the accurate stochastic computation of the series coefficients that suffers from the fermionic sign problem. The second difficulty is the resummation of the series whose success depends on the structure of the physical observable expressed in the complex plane of the expansion parameter, e.g. the onsite repulsion U in the Hubbard model. I will discuss how these two issues can be addressed and, in particular, how the freedom to choose the non-interacting starting point of the theory can be used to construct more efficient perturbation series and directly investigate broken-symmetry phases. I will illustrate these developments with calculations performed in different regimes of the Hubbard model.