Equation of state of the unitary gas: turning the sign problem into a sign blessing Seminar

Expansion in Feynman diagrams is a standard tool of quantum many-body theory. However, one is usually restricted to a few low-order diagrams. Bold diagrammatic Monte Carlo (BDMC) is a new technique to perform the summation of skeleton Feynman diagrams up to high order. We present a cross-validation between BDMC and precision experiments on ultra-cold atoms. Specifically, we focus on the normal-state equation of state of the unitary gas, a prototypical example of a strongly correlated fermionic system. The BDMC method works directly in the thermodynamic limit and with zero-range interactions. The diagrammatic series is found to be strongly oscillating but resummable thanks to sign-alternation of the diagrammatic contributions. The obtained equation of state is in excellent agreement with recent high-precision measurements done at MIT. The contact and the critical temperature can also be extracted. The cross-validation demonstrates that a series of Feynman diagrams can be controllably resummed in a non-perturbative regime using BDMC. This opens the door to the solution of other challenging many-body problems.