Automatic differentiation diagrammatic Monte Carlo

In this talk, we present recent developments in unbiased diagrammatic Monte Carlo methods for fermionic systems. Since, in contrast to conventional quantum Monte Carlo approaches, diagrammatic Monte Carlo methods work directly in the thermodynamic limit, it is necessary to break the appropriate symmetry in the unperturbed Hamiltonian. We show how double (or higher order) expansions can be expressed as a single bare expansion with a renormalized propagator and present, using automatic differentiation tools, an extension of the connected determinant algorithm to efficiently compute such renormalized expansions. This enables, in particular, symmetry-broken expansions around d-wave superconducting states, along with further freedom of choice regarding the starting point of the expansion. Further, we show how within this framework one can automatically measure multiple observables within a single simulation.