### Wandering amongst Feynman Diagrams for strongly correlated fermions

Nikolai Prokof'ev,

UMass Amherst

Feynman diagrams is the most celebrated tool of theoretical
physics. Nearly all key models in physics are subject to the
diagrammatic technique but in the strongly correlated regime it is
often considered useless/hopeless/divergent/(you curse it) and is
reduced to just one (!) lowest-order skeleton graph. I will argue that
diagrammatic expansions form a suitable representation for Monte Carlo
simulations of interacting many-body systems with enormous and yet to
be explored potential. The first application of the new Bold
Diagrammatic Monte Carlo (BDMC) method which samples millions of fully
dressed irreducible Feynman diagrams and extrapolates results to the
infinite diagram order was to the unitary gas of ultra-cold fermions
which have fundamental connections to high-Tc superconductivity,
neutron matter, rich phase diagram, and polaron physics. We observe
excellent agreement with highly accurate thermodynamic data from MIT
for 6Li atoms everywhere in the normal phase. I will also discuss how
BDMC works for models of frustrated quantum magnetism and the Fermi
Hubbard model.