Diagrammatic Monte Carlo Explained

In mathematical physics, the diagrammatic Monte Carlo method is based on stochastic summation of Feynman diagrams with controllable error bars.^{[1] [2]} It was developed by Boris Svistunov and Nikolay Prokof'ev. It was proposed as a generic approach to overcome the numerical sign problem that precludes simulations of many-body fermionic problems.^[3] Diagrammatic Monte Carlo works in the thermodynamic limit, and its computational complexity does not scale exponentially with system or cluster volume.^[4]

Notes and References

1. Van Houcke. K.. Werner. F.. Kozik. E.. Prokof’ev. N.. Svistunov. B.. Ku. M. J. H.. Sommer. A. T.. Cheuk. L. W.. Schirotzek. A.. 2012-03-18. Feynman diagrams versus Fermi-gas Feynman emulator. Nature Physics. En. 8. 5. 366–370. 10.1038/nphys2273. 1745-2473. 1110.3747. 53412117 .
2. Prokof’ev. Nikolay. Svistunov. Boris. 2007-12-18. Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome. Physical Review Letters. 99. 25. 250201. 10.1103/PhysRevLett.99.250201. 18233498. cond-mat/0702555. 42616665 .
3. Rossi . R. . Prokof'ev . N. . Svistunov . B. . Van Houcke . K. . Werner . F. . 2017-04-01 . Polynomial complexity despite the fermionic sign . EPL (Europhysics Letters) . 118 . 1 . 10004 . 10.1209/0295-5075/118/10004 . 0295-5075. 1703.10141 . 17929942 .
4. Houcke. Kris Van. Kozik. Evgeny. Prokof'ev. N.. Svistunov. B.. 2010. Diagrammatic Monte Carlo. Physics Procedia. en. 6. 95–105. 10.1016/j.phpro.2010.09.034. 0802.2923 . 1875-3892. 1854/LU-3234513. 16490610 . free.