Determinant Diagrammatic Monte Carlo for the Self-Energy

Controlled calculations of many-fermion properties by diagrammatic Monte Carlo methods in strongly correlated regimes has been particularly challenging due to the divergence of the bare series and misleading convergence of the skeleton series. With the Hubbard model as an example, we implement a determinant diagrammatic Monte Carlo method for summing irreducible diagrams for the fermionic self-energy directly in the thermodynamic limit. Our approach allows to compute the self-energy in the momentum and Matsubara frequency space up to unprecedentedly high diagram orders, which enables the application of a broad range of analytic continuation methods leading to accurate results in strongly correlated regimes.