Diagrammatic Monte Carlo

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]

References

^ 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. 8 (5): 366–370. arXiv:1110.3747. doi:10.1038/nphys2273. ISSN 1745-2473. S2CID 53412117.
^ 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. arXiv:cond-mat/0702555. doi:10.1103/PhysRevLett.99.250201. PMID 18233498. S2CID 42616665.
^ 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. arXiv:1703.10141. doi:10.1209/0295-5075/118/10004. ISSN 0295-5075. S2CID 17929942.
^ Houcke, Kris Van; Kozik, Evgeny; Prokof'ev, N.; Svistunov, B. (2010). "Diagrammatic Monte Carlo". Physics Procedia. 6: 95–105. arXiv:0802.2923. doi:10.1016/j.phpro.2010.09.034. hdl:1854/LU-3234513. ISSN 1875-3892. S2CID 16490610.

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[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. 8 (5): 366–370. arXiv:1110.3747. doi:10.1038/nphys2273. ISSN 1745-2473. S2CID 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. arXiv:cond-mat/0702555. doi:10.1103/PhysRevLett.99.250201. PMID 18233498. S2CID 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. arXiv:1703.10141. doi:10.1209/0295-5075/118/10004. ISSN 0295-5075. S2CID 17929942.

[4] Houcke, Kris Van; Kozik, Evgeny; Prokof'ev, N.; Svistunov, B. (2010). "Diagrammatic Monte Carlo". Physics Procedia. 6: 95–105. arXiv:0802.2923. doi:10.1016/j.phpro.2010.09.034. hdl:1854/LU-3234513. ISSN 1875-3892. S2CID 16490610.

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