Feynman diagrams versus Fermi-gas Feynman emulator


Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by the intricate quantum statistics at play. Here we present a cross-validation between a new theoretical approach, bold diagrammatic Monte Carlo1,2,3, and precision experiments on ultracold atoms. Specifically, we compute and measure, with unprecedented precision, the normal-state equation of state of the unitary gas, a prototypical example of a strongly correlated fermionic system4,5,6. Excellent agreement demonstrates that a series of Feynman diagrams can be controllably resummed in a non-perturbative regime using bold diagrammatic Monte Carlo.

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Figure 1: Bold diagrammatic Monte Carlo
Figure 2: Cross-validation between resummation procedure and experiment at β μ=+1.
Figure 3: Constructing the EOS from in situ imaging.
Figure 4: Equation of state of the unitary Fermi gas in the normal phase.


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We thank R. Haussmann for providing propagator data from refs 15, 21 for comparison, and the authors of refs 11, 13, 22, 23 for sending us their data. This collaboration was supported by a grant from the Army Research Office with funding from the Defense Advanced Research Projects Agency (DARPA) Optical Lattice Emulator program. Theorists acknowledge the financial support of the Research Foundation Flanders (FWO) (K.V.H.), National Science Foundation (NSF) grant PHY-1005543 (University of Massachusetts group), Swiss National Science Foundation (SNF) Fellowship for Advanced Researchers (E.K.), and l’Institut Francilien de Recherche sur les Atomes Froids (IFRAF) (F.W.). Simulations ran on the clusters CM at UMass and Brutus at ETH. The MIT work was supported by the NSF, AFOSR-MURI, ARO-MURI, Office of Naval Research (ONR), DARPA Young Faculty Award, an AFOSR Presidential Early Career Award for Scientists and Engineers (PECASE), the David and Lucile Packard Foundation, and the Alfred P. Sloan Foundation.

Author information

K.V.H. (theory) and M.J.H.K. (experiment) contributed equally to this work. K.V.H., F.W., E.K., N.P. and B.S. developed the BDMC approach for unitary fermions; the computer code was written by K.V.H. assisted by F.W.; simulation data were produced by F.W., E.K. and K.V.H.; M.J.H.K., A.T.S., L.W.C., A.S. and M.W.Z. all contributed to the experimental work and the analysis. All authors participated in the manuscript preparation.

Correspondence to K. Van Houcke.

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Van Houcke, K., Werner, F., Kozik, E. et al. Feynman diagrams versus Fermi-gas Feynman emulator. Nature Phys 8, 366–370 (2012). https://doi.org/10.1038/nphys2273

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